The Birth of String Theory Edited by Andrea Cappelli, Elena Castellani, Filippo Colomo and Paolo Di Vecchia Index More Information

Cambridge University Press 978-0-521-19790-8 - The Birth of String Theory Edited by Andrea Cappelli, Elena Castellani, Filippo Colomo and Paolo Di Vecchia Index More information

Index

Abrikosov–Nielsen–Olesen vortex, 267, 544 anticommuting variables, 195, 335, 338, 351, action 364–370, 376, 380, 381–384, 395, 409, 416, bosonic string, 586–589 435, 606, 611, 614, 617 Nambu–Goto, 30, 31, 156, 171–172, 230–231, Arvis, Jean-François, 432 238, 250, 251, 266, 280, 285, 298, 305, 369, Aspen Center for Physics, 52, 54, 184, 185, 186, 255, 409, 410, 414, 442, 443, 445, 447, 448, 451, 256, 280, 355, 356, 357, 364, 386, 479, 500, 460, 478, 479, 484, 486, 527, 587, 604 532, 533, 534, 536, 538 quadratic, 171, 238, 443, 590, 604 asymptotic freedom, 38, 199, 239, 256, 352, 356, 428, σ-model, 50, 316, 321, 442–443, 485, 518, 519, 431, 529, 544, 548, 572 538, 546 Atiyah, Michael, 257 point particle, 228–230, 486–487, 586–587 superstring Baker–Campbell–Hausdorff formula, 162, 601 Green–Schwarz, 517–518, 535–536 Balachandran, Aiyalam P., 212, 361, 374 quadratic, 44, 342, 409, 434, 443, 485, 605, 613 Bardakci, Korkut, 25, 182, 196, 214, 332, 344, 349, σ-model, 442–444, 474–481, 484–488, 518, 546, 375, 376, 384, 393–404, 564 588 Bardeen, William A., 54, 536 supersymmetric point particle, 442 Bars, Itzhak, 355 Ademollo et al. collaboration, 200, 205, 208–212, Becchi, Carlo M., 520 216, 289, 332, 450–454 Becchi–Rouet–Stora–Tyutin quantization, see Ademollo, Marco, 100–115, 174, 216, 450 quantization, BRST Adler, Stephen L., 573 Bekenstein, Jacob D., 560 Adler–Bell–Jackiw anomaly, see chiral anomaly Belavin, Alexander A., 394, 403, 547, 549, 556, ADONE, at Frascati INFN laboratories, 173 563 AdS spacetime, 561, 562 Berezinsky, Vadim, 544 AdS/CFT correspondence, 48, 55, 98, 119, 198, 200, Bergmann, Peter G., 361 222, 312, 322, 323, 432, 536, 548, 549, Berkeley, University of California, 4, 25, 38, 39, 43, 561–563 173, 181, 185, 195, 198, 246, 256, 312, 313, affine Lie algebra, 344–345, 375, 396–399, 556, 563, 346, 347, 357, 376 564 beta function, 24, 40, 114, 137, 268, 278, 314, Aharonov, Yakir, 262 579–581 Alessandrini, Victor, 191, 239, 253, 289, 347, 414 Bethe–Salpeter equation, 122, 459 Alvarez, Orlando, 432 Bianchi, Massimo, 565 Alvarez-Gaume,´ Luis, 54, 523, 524, 554 Bjorken, James D., 31, 118, 431 Amati, Daniele, 4, 65, 191–192, 198, 199, 239, 240, Black Hole entropy, 559–561 241, 245, 253, 256, 288, 347, 349, 353, 355, Block–Nordsieck approximation, 172 357, 373, 407, 408, 411, 474, 478, 490, 560 bootstrap, see Chew–Frautschi bootstrap approach amplitude, see scattering amplitude bosonic sector, see Neveu–Schwarz sector anomaly, see chiral anomaly, conformal anomaly bosonization, 398, 400–402, 536 anti de Sitter spacetime, see AdS spacetime Bouchiat, Claude, 191, 373, 408, 454, 490, 491, 492, anti de Sitter/conformal field theory correspondence, 496 see AdS/CFT correspondence boundary conditions, 224, 226

626

© in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-19790-8 - The Birth of String Theory Edited by Andrea Cappelli, Elena Castellani, Filippo Colomo and Paolo Di Vecchia Index More information

Index 627

Dirichlet, 225, 226, 289, 290, 388, 530, 531 Chandrasekhar, Subrahmanyan, 559 Neumann, 91, 226, 228, 300, 301, 315, 388, 556, Chang, Lay N., 280 590 Chapline, George F., 524 periodic, 226, 556, 564 Chern–Simons theory, 566, 567 twisted, see also supersymmetry breaking, 348, Chew, Geoffrey F., 20–22, 38, 67, 91, 104, 117, 118, 441, 476 276, 277, 313, 346 brane, see Dirichlet brane Chew–Frautschi bootstrap approach, 39, 68, 68, 91, Breit–Wigner amplitude, 91, 92–93, 95, 98, 278, 313, 96, 117, 129–130, 194, 203, 565, 579 577–578 exact solution, 565–566 Brink, Lars, 9, 11, 45, 51, 53, 216, 253, 273, 349, 350, Chicago, University of, 4, 276, 353, 363, 369 355, 384, 442, 450, 474–482, 484, 486, 487, chiral anomaly, see also fermion, chiral, 52–54, 407, 498, 513, 529, 534, 593 521–522, 554 Brink–Di Vecchia–Howe–Deser–Zumino action, see cancellation, 521–525, 554–555 action, σ -model Green–Schwarz cancellation mechanism, 31, Brookhaven National Laboratories, 193 54–55, 119, 357, 468, 522–525, 534–538, Brout–Englert–Higgs mechanism, see Higgs 555 mechanism chiral symmetry, 572 Brower, Richard C., 45, 76, 169, 241–249, 288, 298, Ciafaloni, Marcello, 560 312–323, 349, 393 City College, see NYU BRST quantization, see quantization, BRST Clavelli, Louis, 187, 193–197, 200, 280, 349, 363, 370, 374, 381 Cabibbo angle, 101, 570 Coleman, Sydney R., 245 Cabibbo, Nicola, 569, 570 Collins, Peter V., 380 Calabi–Yau compactification, 55, 525, 539, Collop, David, 379 556 compactification, see Kaluza–Klein compactification California Institute of Technology, Pasadena, see confinement, 431 Caltech conformal Callan, Curtis, 245 algebra, see Virasoro algebra Callan–Treiman relation, 104 anomaly, 166, 252, 303, 519, 520, 594 Caltech, 4, 45, 47, 51, 52, 129, 173, 389, 480, dimension, 149 481, 498, 500, 501, 503, 533, 534, 536, factor, 519, 520 538 field theory, 149, 394–403, 549, 556, 563, 564, Campbell, David, 379 565 Candelas, Philip, 55, 525, 539, 555 gauge, see gauge choice, conformal Caneschi, Luca, 27, 215, 349 invariance, 46, 145–147, 166–169, 171, 182, 185, Cappelli, Andrea, 564 192, 215, 223, 237, 264, 271, 285–288, 298, Capri, NATO Summer School, 434 302–306, 317–321, 322, 364, 369, 381, Cardy, John L., 379, 382, 564 394–403, 408, 461, 462, 533, 544, 547–549, Carlitz, Robert, 529 589, 590, 598, 600, 604 Casimir minimal models, 547, 563, 564 energy, 449 primary field, see vertex operator invariant, 398, 538 representation, 166, 381, 389, 397, 403, 415, 556, central charge, see central extension 563 central extension, see also affine Lie algebra, 27, Corrigan, Edward, 12, 253–255, 289, 290, 339, 348, 43, 102, 147, 150, 166, 298, 316, 320, 322, 350, 355, 378–390, 414, 415, 478, 529 339, 341, 344, 358, 367, 380, 394, 395, 397, coset construction, see also affine Lie algebra, 357, 400, 401, 402, 448, 512, 519, 520, 563, 399–400 609 counterterms, see also renormalization, 481, 497, 532 CERN, 4, 45, 52, 65, 88, 191, 193, 198–199, 216, Courant Institute, 407 239–256, 273, 288, 316, 346–357, 382, 389, covariance, see also Lorentz invariance, 53–54, 146, 393, 410, 411, 436, 450, 468, 470, 475–479, 149, 164, 209, 228, 237, 250–253, 285, 299, 490–491, 498, 501, 504, 529, 532, 553 302, 306, 307, 365, 394, 396, 439, 452, 463, CFT, see conformal field theory 465, 488, 533, 535–536, 537, 547 Chan, Hong-Mo, 214, 284, 331, 333, 347, 349, 393, CP factors, see Chan–Paton factors 414 Cremmer, Eugene,` 223, 349, 355, 411, 423, 454, 455, Chan–Paton factors, 40, 47, 160, 186, 331, 333–334, 490–494, 498, 500, 502, 511, 513, 514 395, 424, 425 Creutz, Michael, 431

628 Index

critical dimension Dirac–Ramond equation, 43, 336, 367, 368, 369 bosonic string, 30, 42, 45, 48, 142, 143, 144, 145, Dirichlet brane, 49, 52, 200, 290, 370, 432, 440, 442, 147, 171, 172, 196, 199, 234, 246, 247, 249, 469, 504, 527, 529, 530, 531, 548–549, 251, 254, 273, 290, 298, 302, 320, 332, 375, 556–557, 559, 561, 565 449, 464, 488, 520, 530, 582, 583 dispersion relation, 106, 117, 276, 277, 283, 407, 459, superstring, 45, 127, 210, 247, 253, 255, 298, 332, 575, 576 341, 388, 449, 453, 455, 610 divergences, see also renormalization, 241, 275, 303, crossing symmetry, see scattering amplitude 307, 323, 363, 373, 374, 429, 430, 452, 475, current algebra, see also affine Lie algebra, 46, 90, 497, 498, 499, 512, 514, 525, 534, 535, 593 102–109, 174, 208, 323, 332, 334, 335, 379, Dolen, R., 8, 95 393–403, 475, 528, 547, 569–573 Dolen–Horn–Schmid duality, 22, 24, 29, 68, 77, 91, curvature tensor 95, 96, 97, 98, 100, 108, 118, 123, 130, 142, Ricci, 538, 556 157, 180, 181, 204, 208, 277, 313, 366, 528, Riemann, 624 581, 582 Cushing, James T., 67 Dothan, Joe, 23 Cutkosky rules, 239 DRM, see model, dual resonance DRM amplitude, see also Koba–Nielsen amplitude, D’Adda, Alessandro, 174, 205, 216, 450 Veneziano amplitude, 43, 137–143, 157, D’Auria, Riccardo, 174, 205, 216, 450 158–163, 210, 238, 249, 294, 296, 451, D-brane, see Dirichlet brane 600–602 Dahmen, Hans, 23 Drummond, Ian, 240, 379, 390, 415 Dalitz, Richard, 119, 347 duality, 27, 28, 39, 40, 42, 104, 110–112, 122, 158, DAMTP, 239, 250, 346, 357, 379, 416, 502, 539 181, 236, 264, 278, 284, 347, 379, 460, 491, Dancoff, Sidney M., 116 498, 528, 529 Dashen, Roger, 245, 256 among string theories, see superstring dualities David, François, 547 diagram, 31, 97, 98, 137, 138, 139, 140, 141, 142, DDF states, 27, 30, 152, 169–170, 234, 244–247, 249, 144, 159, 191, 214, 276, 286, 333, 351 256, 298, 317–321, 350, 353, 597 planar, see also Dolen–Horn–Schmid duality, 139, De Alfaro, Vittorio, 107, 214 182, 460 De Sitter spacetime, 549 self-dual fields, equations, 545, 549 Del Giudice, Emilio, 9, 76, 152, 173, 205, 216, 234, T-type, 53, 493, 500 317, 337, 352, 450 Duff, Michael J., 514 Del Giudice–Di Vecchia–Fubini operators, see DDF Durham University, 240, 246, 253, 254, 256, 284, states 349, 356, 384, 385, 389, 416, 480 Della Selva, Angelo, 215 Durhuus, Bergfin, 488 Department of Applied Mathematics and Theoretical Dynkin index, 397 Physics, Cambridge UK, see DAMTP Dyson, Freeman, 116 Deser, Stanley, 50, 442, 445, 486 DeWitt, Bryce, 477 Ecole´ Normale Superieure,´ Paris, see ENS and DHS duality, see Dolen–Horn–Schmid duality LPTENS Di Vecchia, Paolo, 9, 76, 152, 156–175, 205, 216, Eichten, Estia J., 431 234, 238, 253, 337, 349, 352, 384, 442, 450, einbein, see also vierbein, 486, 587 479–481, 484–488 Einstein diffeomorphisms, see reparameterization invariance action, 428, 445 dilatino, 516, 523 medal, 33 dilaton, 46, 307, 425, 452, 516, 596, 624 theory of gravity, 17, 48, 49, 131, 179, 180, 199, Dirac 204, 205, 211, 262, 323, 361, 378, 425, brackets, 256 428–429, 430, 439, 442, 444, 461, 462, equation, 42, 116, 243, 278, 335, 336, 337, 340, 464–470, 480, 484, 493, 499, 500, 512, 527, 350, 364, 367, 465, 480, 613 548, 556, 624 fermion, see fermion Einstein, Albert, 462, 499, 624 matrices, 42, 44, 85, 101, 278, 336, 340, 364, 367, Ellis, John R., 379 380, 382, 444, 445, 605, 608, 611, 614 energy-momentum tensor, see also conformal medal, 56, 258, 358, 505, 539 invariance, 343, 369, 443, 448, 465, 484, 485, Dirac, Paul A. M., 100, 212, 232, 257, 286, 288, 362, 520, 588, 604, 605, 607 378, 527, 569 trace anomaly, see conformal anomaly Dirac–Born–Infeld action, 527 ENS, 51, 373, 374, 389, 454, 455, 492, 496, 500

Index 629

Erice Summer School, 22, 504 Frishman, Yitzhak, 393 European Centre for Nuclear Research, Geneva, see Fritsch, Harald, 349 CERN Froissart bound, 118 Fubini, Sergio, 4, 9, 22, 23, 25, 26, 27, 74, 76, 107, F-theory, 49, 200 118, 135, 148, 149, 173, 205, 208, 212, factorization, 25, 26, 27, 28, 41, 143, 147, 157, 214–216, 234, 245, 256, 287, 335, 348, 363, 158–163, 173, 183, 186, 191, 194, 196, 198, 450, 474 200, 210, 214, 278, 280, 295–297, 314, 315, Fubini–Veneziano operators, 26–27, 135, 148, 149, 362, 369, 374, 375, 387, 410, 447, 452, 460, 172, 184, 191, 210, 222, 232, 287, 335, 362, 463, 491, 497, 498 374, 379, 387, 394, 408, 447, 451, 460, 469 Faddeev, Ludwig D., 520 Fuchs, Dmitry B., 563 Faddeev–Popov functional integral, see quantization, path-integral ghosts, 297, 321, 520 Furlan, Giuseppe, 103, 214 quantization, see quantization, path-integral Fairlie, David B., 11, 71, 238, 240, 246, 250, 267, gamma function, 106, 137, 181, 579–581 270, 271, 283–291, 355, 356, 384, 386, 389, gauge choice 414, 416, 480 conformal, 171, 443, 448, 451, 485, 519, 589, 590, Farrar, Glennys, 355 591, 592, 596, 598, 604 Fayet, Pierre, 454 covariant, 44, 171, 223, 232, 233, 307, 352, 488, Feigin, Boris L., 563 519 Fermi National Acceleration Laboratory, see Fermilab light-cone, 172, 200, 256, 298, 307, 410, 437, 529, Fermi theory, 83, 427, 429, 569, 571 591, 592, 610 Fermi, Enrico, 569 orthonormal, see also gauge choice, conformal, Fermilab, 193, 194, 195, 362–368, 369, 374, 375, 376 232, 233, 234, 251, 589 fermion, 433–434 gauge fixing, see gauge choice chiral, 46, 50, 54, 255, 314, 356, 433–434, 521, 533 gauge particle, 50, 53, 169, 352, 353, 424, 425, 572, Dirac, 85, 340, 386, 433–434, 469, 571, 611, 613 594 in d dimensions, 433–434 gauge symmetry, 40, 48, 158, 164, 228, 230, 233, 237, Majorana, 44, 433–434, 455, 485, 611 334, 341, 344, 426, 434, 461–463, 498, 499, Majorana–Weyl, 51, 200, 341, 396, 433–434, 438, 514, 521, 553, 554, 555, 559, 564, 589, 604, 455, 513, 515, 517, 611 624 Ramond, 47, 255, 383, 478, 498 residual, 233, 341, 342, 589, 604, 612 Weyl, 395, 433–434, 435, 441, 454, 521, 611 gauge theory fermionic sector, see Ramond sector Abelian, see also QED, 476 Ferrara, Sergio, 50, 216, 445, 450, 454, 480, 502 anomaly, see chiral anomaly FESR, see sum rule, finite energy coupling constant, 38, 104, 202, 424, 425, 428, 513, Feynman 545, 553, 621, 623, 624 diagram, 21, 22, 40, 48, 84–88, 122–124, 182, 237, non-Abelian, 47, 130, 156, 179, 187, 239, 257, 264, 239, 264, 266, 269–272, 277, 284, 286, 312, 321, 322, 355, 370, 378, 401, 402, 407, 408, 313, 348, 353, 408, 410, 461, 462, 463, 468, 410, 423, 425, 427, 431, 464, 467, 468, 476, 477, 478, 492, 528, 546, 570 477, 493, 499, 529, 544, 546, 547, 549, 571, parton model, 187, 196, 205, 314, 316, 317, 322, 620, 621, 623, 624 349, 428, 530 nonperturbative, 323, 431, 432, 557, 561 path-integral, see quantization on a lattice, 431, 432, 468, 544, 545, 562 Feynman, Richard P., 349, 354, 355, 476, 569 supersymmetric, 55, 200, 322, 357, 435, 436, 455, Feynman–Gell–Mann V − A theory, 101, 569 481, 501, 525, 545, 548, 556, 557, 561, 562 Fierz identities, 385, 481, 487 gauge/gravity correspondence, see AdS/CFT fishnet diagram, 31, 122, 185, 221, 271–272, 286, correspondence 466 Gell-Mann matrices, 101, 397, 571 FNAL, see Fermilab Gell-Mann, Murray, 4, 22, 45, 88, 89, 101, 102, 123, Foster, A. E., 361 129–131, 204, 209, 253, 348, 349, 355, 393, Fradkin, Efim S., 409 474, 477, 480, 481, 538, 569, 570, 571 Frampton, Paul, 253, 273, 278, 349, 380 general relativity, see Einstein theory of gravity Freedman, Daniel Z., 50, 445, 454, 502 Georgi, Howard M., 428 Frenkel, Igor, 357, 402 Gepner, Doron R., 564 Freund, Peter G. O., 96, 122, 127, 350, 380 Gervais, Jean-Loup, 6, 44, 66, 191, 332, 355, Friedan, Daniel, 54, 341, 538, 556, 564 407–411, 443, 453, 454, 479, 490, 491–492

630 Index

ghost, 150 Haag, Rudolf, 512 Faddeev–Popov, see Faddeev–Popov ghosts hadron spectrum, 19, 21, 46, 88–91, 453 no-ghost theorem, 27, 44, 76, 170, 241–249, 252, Hagedorn transition, 26, 32, 279, 527, 528, 595 298, 312, 316–321, 354, 385, 476, 478 Hagedorn, Rolf, 595 state, 25, 26, 27, 158, 163–170, 181, 184, 185, 209, Halpern, Martin B., 182, 196, 332, 344, 376, 393–404, 210, 237, 289, 351, 382, 409, 415, 491, 520 564 Girardello, Luciano, 503 Hansen, Klud, 271 Glashow, Sheldon L., 38, 427, 428, 571 Hara, Osamu, 221 Glashow–Weinberg–Salam model, see Standard Hara, Yasuo, 467 Model Harari, Haim, 96 Gliozzi, Ferdinando, 6, 14, 66, 73, 174, 216, 243, 349, Harari–Rosner duality diagram, see also duality 356, 363, 422, 437, 447–456, 501, 611 diagram, 22, 29, 96, 97, 124, 157, 186, Gliozzi–Scherk–Olive projection, 30, 50, 51, 53, 212, 349 307, 341, 430, 437–439, 454–456, 501, 502, Harte, John, 368 515, 521, 529, 531, 554, 564, 610–612 Harvey, Jeffrey A., 55, 525, 538, 555 glueball, 32, 321, 323, 528, 562 Hawking, Stephen W., 347, 559 gluon, 31, 32, 255, 317, 321, 467, 493, 547, 566, 572, Heineman prize, 33, 56, 504, 539 623, 624 Heisenberg, Werner K., 4, 67, 129, 173, 203, 204, Goddard, Peter, 5, 73, 76, 150, 152, 222, 233, 208, 272, 275, 346, 348 236–257, 288, 317, 318, 348, 349, 355, 357, helicity, 137, 158, 277, 433, 436, 613 379, 382, 384, 385, 386, 478, 529, 538, 564 Higgs mechanism, 267, 284, 321, 428, 466, 503 Goddard–Goldstone–Rebbi–Thorn quantization, see holography, 200, 470, 549, 561 quantization holonomy, 290 Goebel, Charles J., 214 Honerkamp, Josef, 353, 477 Goldberger, Marvin L., 130, 245, 276 Horn, David, 8, 95 Goldberger–Treiman relation, 208 Horowitz, Gary T., 55, 525, 539, 555 Goldstone, Jeffrey, 5, 73, 150, 152, 222, 233, 250, Horsley, Roger, 256 253, 257, 348, 356, 378, 476, 529 Howe, Paul S., 442, 525 Goldwasser, Edwin L., 194 Huttunen Foundation, 414 Golfand, Yuri A., 434 hypercharge, 88, 89 Gordon, David, 9, 193, 287, 363, 374, 476 Goto, Tetsuo, 5, 11, 73, 136, 221, 238 IAS, 188, 199, 256, 258, 281, 357, 368, 375, 376, 529, Gottfried, Kurt, 431 539 Gourdin, Michel, 490, 491 ICTP, 362 Grand Unified Theories, 120, 352, 427–428, 469, 553 IHES, 408 Grassmann variables, see also anticommuting Iliopoulos, Jean, 454 variables, 289, 369, 479, 487, 536, 606 IMF, 262–263 gravitino, 50, 52, 436, 442, 444, 445, 454, 487, 503, infinite momentum frame, see IMF 513, 516, 522, 523, 531 instanton, 481, 488, 529, 530, 545 graviton, 47, 50, 53, 127, 131, 136, 199, 210, 212, Institut des Hautes Etudes´ Scientifiques, 323, 348, 352, 425, 430, 436, 442, 451, 464, Bures-sur-Yvette, see IHES 465, 467, 499, 504, 516, 522, 534, 537, 596, Institute of Advanced Study, Princeton, see IAS 600, 624 International Center for Theoretical Physics, Trieste, Green, Michael B., 7, 15, 45, 52, 53, 54, 67, 119, 126, see ICTP 129, 192, 197, 290, 348, 355, 357, 368, 468, Intersecting Storage Ring, CERN, see ISR 504, 515, 517, 523, 525, 527–539, 555 Ising model, 546, 564, 565 Green–Schwarz light-cone formalism, see also action, isospin, 88, 89, 90, 101, 107, 109, 109, 117, 160, 267, Green–Schwarz, 53, 54, 307, 514–518 268, 333, 334, 434, 491, 570 Grisaru, Marc, 348 ISR, 31 Gross, David J., 38, 41, 55, 199, 374, 428, 469, 497, Itzykson, Claude, 564 525, 529, 538, 555, 560 Iwasaki, Yoichi, 410 GSO projection, see Gliozzi–Scherk–Olive projection Gubser, Steven S., 548 Jacobi identity, 51, 438, 455, 502, 612, 616 Gupta–Bleuler quantization, see quantization, 152 Jevicki, Antal, 467, 468 Gursey,¨ Feza, 368, 370 Jones, Keith, 284 GUT, see Grand Unified Theories Julia, Bernard, 511, 513, 514

Index 631

Kac determinant, 242, 320 nonplanar, 28, 29, 42, 97, 99, 142, 143, 144, 170, Kac, Victor G., 563 185–187, 200, 247, 491, 523, 524, 525, 537 Kac–Moody algebra, see also affine Lie algebra, 256, planar, 28, 143, 184, 270–290, 491, 523, 537 397, 402, 453, 480 Lopuszanski, Jan T., 512 Kajantie, Keijo, 414 Lorentz invariance, 84, 163, 172, 173, 226, 228, 233, Kaku, Michio, 355, 376, 411, 464, 492, 498 234, 252, 278, 289, 299, 302, 305, 319, 354, Kalb–Ramond field, 370 366, 367, 397, 398, 444, 449, 469, 492, 519, Kaluza–Klein compactification, 49, 54, 56, 199, 280, 520, 533, 556, 592, 594, 596 430, 439–441, 493 503, 513, 514, 533, 534, Lovelace, Claud, 5, 9, 42, 43, 75, 127, 144, 187, 191, 554 195, 198–200, 215, 241, 243, 247, 251, 252, Kanazawa, Akira, 459 254, 264, 289, 297, 334, 347, 348, 349, 350, Kavli Institute of Theoretical Physics, Santa Barbara, 353, 354, 370, 393, 415, 460, 497, 556 see KITP Lovelace–Shapiro amplitude, 195, 332, 334–335, 338, Kazakov, Vladimir A., 547 375, 585 Kent, Adrian P. A., 564 LPTENS, see also ENS, 492, 500, 503 Kikkawa, Keiji, 280, 297, 355, 410, 411, 467, 469, 492 LPTHE, see also Orsay, 407, 408 Kinoshita, Toichiro, 431 Luscher,¨ Martin, 432 KITP, 470 KK compactification, see Kaluza–Klein M-theory, 49, 51, 322, 556–557 compactification Maiani, Luciano, 245 Klebanov, Igor R., 548 Majorana fermion, see fermion KN amplitude, see Koba–Nielsen amplitude Makeenko, Yuri, 546 Knizhnik, Vadim G., 547, 564 Maldacena conjecture, see AdS/CFT correspondence Koba, Ziro, 8, 214, 268, 269–271, 280 Maldacena, Juan M., 98, 561 Koba–Nielsen amplitude, 139–141, 158, 185, 237, Manassah, Jamal, 368 243, 269, 271–272, 285, 286, 288, 289, 331, Mandelstam variables, see also scattering amplitude, 379, 380, 387, 408, 414, 415, 601 24, 39, 86, 88, 98, 104, 105, 109, 137, 267, Kogut, John B., 431 276, 362, 528, 573, 579, 581, 622 Komaba campus, University of Tokyo, 465, 467 Mandelstam, Stanley, 4, 25, 38, 39, 43, 86, 198, 223, Kosterlitz, John M., 215 255, 256, 294–307, 313, 316, 349, 354, 369, Kuhn, Thomas, 70 376, 379, 387, 393, 401, 410, 432, 474, 479, 498, 545 Laboratoire de Physique Theorique´ et Hautes Mansouri, Freydoon, 280 Energies, Orsay, see LPTHE Manton, Nicholas S., 256, 524 Laboratoire de Physique Theorique,´ Ecole´ Normale Martinec, Emil J., 55, 341, 525, 538, 555 Superieure,´ Paris, see LPTENS Mason, Antony, 380 landscape of string vacua, 558–559 mass-shell condition, 38, 86, 130, 425, 573, 602 Lane, Kenneth D., 431 Massachusetts Institute of Technology, Boston, see Langlands, Robert, 257 MIT Large Electron–Positron collider, CERN, see LEP Matsuda, Satoshi, 368 Large Hadron Collider, CERN, see LHC McDowell, Samuel W., 368 Le Bellac, Michel, 239, 347 McFarlane, Alan, 361 Lebedev Institute, Moscow, 409 Mende, Paul F., 560 Lederman, Leon M., 239 metric tensor Lee, Benjamin W., 370, 407 spacetime, 164, 236, 351, 428, 436, 442, 444, 451, LHC, 188, 436, 549, 553 484 light-cone, 153, 154 world-sheet, 305, 306, 315, 316, 442, 443, 444, coordinates, 172, 233, 262, 298, 300, 302, 317, 342, 518, 519, 520, 531, 546, 588 411, 530, 532, 535, 589, 607 Migdal, Alexander A., 544, 546 gauge, see gauge choice, light-cone Minami, Masatsugu, 462 Likhtman, Eugeny P., 434 Minimal Supersymmetric Standard Model, 436, 553 Linstrom,¨ Ulf, 525 MIT, 4, 25, 27, 173, 205, 214, 316 Liouville theory, 306, 322, 468, 520, 546–548 Mobius¨ loop diagram, 41, 53, 55, 87, 88, 125, 143–145, 157, invariance, 139–141, 145, 158–160, 182, 183, 186, 175, 180, 182–187, 198, 414–416, 478, 529, 237, 285, 381, 415, 460 533 strip, 54, 240, 523, 537, 538

632 Index

model Nicodemi, Francesco, 174, 208–212, 216, 450 analogue, 141, 222, 237, 238, 243, 250, 286–290, Niels Bohr Institute, Copenhagen, 175, 266, 272, 273, 297, 375, 386, 408, 447, 448 356, 410, 486, 488 dual pion, see model, Neveu–Schwarz, 338 Nielsen, Holger B., 5, 8, 11, 71, 72, 136, 198, 214, dual quark, 395, 403 237, 238, 250, 264, 266–273, 280, 286, 349, dual resonance, 18, 25–27, 69, 98, 99, 113, 350, 356, 384, 408, 414, 447, 476, 478, 479, 137–155, 157–163, 174, 180, 205–209, 210, 593 214, 221, 222, 223, 226, 231, 232, 233, 234, Nilsson, Bengt E.W., 514 254, 331, 333, 335, 337, 347, 356, 363, 368, no-ghost theorem, see ghost 423, 426, 447, 585, 600–602, 609, 620 Noether current, 342, 480, 570, 571, 606, 615 interactions, 211, 450, 597–600 nonrenormalizability, see renormalization physical states, see also DDF states, 73, 76, Nordita, 175, 286, 479–481, 486, 488 150–153, 167–170, 174, 228, 231–234, 336 normal ordering, 149, 161, 299, 315, 338, 398, 597, Lovelace–Shapiro, see Lovelace–Shapiro amplitude 598, 599, 608 Neveu–Schwarz, 289, 297, 299, 332, 338–339, 351, NS sector, see Neveu–Schwarz sector 380, 462, 584 Nussinov, Shmuel, 185 Ramond, 289, 297, 299, 332, 335–337, 351, 382, Nuyts, Jean, 257, 357, 362, 374, 490 396 NYU, 407, 409, 410, 498 Ramond–Neveu–Schwarz, 42–45, 130, 157, 175, 187, 191, 196, 210, 212, 244, 255, 273, 304, Olesen, Paul, 267, 272, 356, 466, 488 332, 339–341, 351, 375, 382, 408, 434, 436, Olive, David I., 6, 9, 12, 14, 55, 66, 73, 239, 240, 437, 442, 443, 444, 449, 454, 478, 479, 491, 253, 254, 256, 257, 286, 339, 346–358, 379, 492, 501, 511, 515, 529, 533, 537, 605, 609 380, 382, 385, 386, 389, 390, 411, 414, 415, spectrum of, 339, 437, 610 422, 437, 455, 467, 475, 476, 479, 529, 564, Shapiro–Virasoro, 141, 142, 143, 150, 199, 205, 611 210, 423, 449, 491, 492 Omnes,` Roland, 410 modular invariance, 187, 199, 357, 439, 531, 534, Ooguri, Hirosi, 567 564, 565, 612 operator monodromy, 395 anticommuting, see anticommuting variables monopole, 355, 357, 529, 545, 557 formalism, see also Fubini-Veneziano operators, ’t Hooft–Polyakov, 257, 355, 388, 416 71, 147–150 Montonen, Claus, 350, 380, 381, 390, 414–416 physical-state, see DDF states Moyal product, 469 O’Raifeartaigh, Lochlainn, 204 MSSM, see Minimal Supersymmetric Standard Model orientifold, 516 multiloop diagram, see loop diagram Orsay, see also LPTHE, 191, 349, 373, 374, 375, multiperipheral model, 347, 373 407, 408, 410, 416, 490, 491, 492, 496, 498, Musto, Renato, 174, 202–206, 216, 450 500 Oskar Klein medal, 33, 371 Nahm, Werner, 513 Nakanishi, Noboru, 463, 465, 468 Pagels, Heinz R., 355 NAL, see Fermilab Pantin, Charles, 380, 390 Nambu, Yoichiro, 4, 5, 11, 72, 73, 136, 238, partially conserved axial current, see PCAC 272, 275–281, 355, 363, 368, 369, 460, 474, partition function, 375, 382, 438, 476, 478, 564, 595, 479 610, 611, 612 Nambu–Goto action, see action, Nambu–Goto partitions of integers, 148, 595 Napolitano, Ernesto, 174, 205, 216, 450 Pasternack, Simon, 182 narrow-resonance approximation, see resonance width Paton, Jack E., 331, 333 Naylor prize, 539 Pauli matrices, 342, 605 Ne’eman, Yuval, 88, 570 Pauli, Wolfgang E., 116, 335 Neveu, Andre,´ 5, 6, 12, 41, 43, 45, 70, 74, 129, 191, PCAC, 103, 181, 573 256, 332, 338, 350, 362, 370, 373–376, 410, Peierls, Rudolf E., 307, 545 416, 430, 454, 475, 490, 496, 499, 529, 605 Petersen, Jens L., 488 Neveu–Schwarz model, see model Peterson, Dale H., 563 Neveu–Schwarz sector, 44, 50, 304, 339, 340, 341, Pettorino, Roberto, 174, 216, 450 342, 396, 437, 438, 454, 478, 501, 529, 605, Picasso, Emilio, 239 607, 608, 609, 610 planar diagram, see duality diagram New York University, see NYU Poincare´ invariance, see Lorentz invariance

Index 633

Polchinski, Joseph, 290, 322, 388, 556 quark, 22, 31, 32, 38, 47, 89, 101, 102, 117, 118, 126, Politzer, David H., 428 186, 209, 283, 380, 427, 428, 467, 493, 521, Polkinghorne, John C., 239, 291, 355, 379, 383, 390 571–573 Polyakov action, see action, σ-model confinement, 19, 32, 38, 118, 119, 431, 468, 481, Polyakov, Alexander M., 15, 50, 66, 76, 145, 147, 545, 572 192, 264, 298, 303, 305, 306, 307, 322, 442, 481, 488, 518, 520, 533, 538, 544–550, 556, R sector, see Ramond sector 563, 594 Ramond model, see model Pomeranchuk Ramond sector, 44, 50, 255, 304, 339, 340, 341, 342, prize, 33 396, 438, 454, 478, 501, 529, 531, 534, 605, theorem, 118 607, 608, 609, 611 Pomeranchuk, Isaak Y., 95, 124 Ramond, Pierre, 5, 12, 43, 70, 129, 193, 195, 197, Pomeron, 28, 32, 46, 76, 93, 95, 96, 97, 124, 126, 144, 210, 212, 243, 288, 332, 335, 349, 350, 371, 184, 187, 191, 194, 195, 196, 199, 241, 248, 374, 375, 381, 389, 479, 480, 481, 529, 605 264, 277, 289, 348, 352, 354, 450, 452, 478, Ramond–Neveu–Schwarz model, see model 491, 497, 499 Rarita–Schwinger field, 454 Ponzano, Giorgio, 256 Rebbi, Claudio, 5, 73, 150, 152, 215, 222, 233, 249, Pope, Christopher N., 514 250, 253, 349, 354 Popov, Victor N., 520 Rees, Martin J., 347 Pradisi, Gianfranco, 565 Regge Princeton University, 40, 191, 194, 199, 256, 374, behaviour, 21, 24, 39, 93–94, 95, 97, 98, 106, 107, 410, 496, 497, 498, 537 113, 180, 181, 194, 195, 204, 209, 239, 263, 269, 313, 459, 528 QCD, 18, 19, 31, 38, 47, 120, 130, 352, 428, 499, 562, pole, see Reggeon 572, 623 trajectories, 20–22, 29, 39, 40, 43, 46, 90, 91, string, 55–56, 119, 312, 317, 321–323, 431–432, 93–97, 106, 108, 110, 117, 137, 141, 148, 165, 528, 562 180, 184, 204, 209, 210, 253, 268, 277, 294, QED, 17, 19, 21, 38, 83, 84–88, 100, 122, 158, 171, 298, 334, 335, 338, 339, 346, 352, 358, 423, 173, 180, 312, 367, 476, 569 426, 427, 431, 448, 449, 497, 499 QFT, see quantum field theory Regge, Tullio, 84, 93, 245, 256 Qiu, Zongan, 564 Reggeon, 39, 84, 92, 93–97, 106, 124–126, 130, 173, quantization 181, 184, 194, 195, 198, 200, 214–216, 239, BRST, 150, 156, 215, 321, 464, 520, 538 241, 267, 277, 283, 347, 381, 410, 415, 449, covariant (old), 165–170, 234, 314–319, 518, 520, 459, 460, 478, 491, 492, 528 596–597 regularization, see also renormalization Goddard–Goldstone–Rebbi–Thorn, 30, 42, 73, 76, ζ -function, 187, 449, 593 150, 152, 170–172, 210, 215, 222, 233–234, Renner, Bruno, 382 249–254, 289, 298, 299, 302, 319, 409, 415, renormalization, 48, 49, 54, 87, 116, 131, 180, 187, 447, 448, 450, 592–596 202, 240, 241, 276, 303, 370, 398, 407, 428, Gupta–Bleuler, 172, 173, 252, 316, 366, 367 429, 464, 478, 499, 529, 533, 538, 544, in QED, see also quantization, Gupta–Bleuler, 569 163–165 renormalization group, 256, 513, 529, 548 light-cone, 42, 76, 150, 152, 172, 233–234, 518, reparameterization invariance, 50, 136, 156, 171, 172, 520, 592–596 205, 211, 222, 230, 231, 232, 234, 285, 306, of gravity, 46–49, 428–429, 464, 466, 467, 477, 410, 426, 439, 442, 448, 451, 479, 480, 484, 493, 499, 500, 535, 547 485, 486, 487, 519, 564, 586, 587, 588, 604 path-integral, 150, 156, 306, 307, 407, 410, 476, Research Institute for Mathematical Sciences, Kyoto, 520 see RIMS covariant, 305–307, 485, 518–521, 597 resonance, 90, 92–97, 335, 577 light-cone, 223, 304–305, 597 width, 99, 143, 576, 578 Polyakov, see quantization, path-integral, covariant Riemann surface, 170, 192, 198, 286, 297, 303, 306, with constraints, 43, 44, 53, 168, 171, 252, 450, 315, 408, 463, 491, 497 479, 485, 486, 487, 536 RIMS, 462, 463 quantum chromodynamics, see QCD RNS model, see model quantum electrodynamics, see QED Rohm, Ryan, 55, 525, 538, 555 quantum field theory, 84–88, 148, 335, 423, 569, Rosner, Jonathan L., 96 620 Rouet, Alain, 520

634 Index

Rubinstein, Hector R., 23, 100, 108, 116–120, 262, Schwinger, Julian S., 116, 362 266, 269, 272 Sciama, Dennis W., 347, 378 Ruegg, Henri, 214, 393 Sciuto, Stefano, 174, 214–216, 349, 450 Rutgers University, 187, 193, 195, 199, 241, 349, 370 Scuola Internazionale Superiore di Studi Avanzati, Rychkov, Vyacheslav S., 549 Trieste, see SISSA Segre, Gino C., 393 S-matrix theory, 19–25, 38–40, 67, 84, 91, 98, 100, Seiberg, Nathan, 545, 557 104, 117, 120, 129–130, 141, 157–169, 174, Serber, Robert, 363 184, 202–205, 208, 209, 210, 238–240, 262, Serpukhov Laboratories, 193 275–278, 283, 295, 306, 313, 362, 380, 407, Shapiro, Joel A., 9, 41, 43, 70, 141, 179–188, 195, 414, 465, 475, 476, 528, 573–576, 620 196, 199, 334, 349, 355, 393, 530 Sagnotti, Augusto, 565 Shapiro–Virasoro amplitude, 210, 243, 464, 465 Saito, Satoru, 215 Shapiro–Virasoro model, see model, Shapiro–Virasoro Sakata model, 102, 118 Shenker, Stephen H., 54, 341, 537, 538, 564 Sakita, Bunji, 6, 44, 66, 195, 214, 272, 332, 355, 363, SISSA, 347 408–411, 443, 467, 468, 479 Skyrme, Tony H. R., 356, 378 Salam, Abdus, 100, 199, 245, 355, 357, 362, 407, 427, SLAC, 38, 45, 64, 92, 118, 185 453, 476, 571 Slansky, Richard, 368 scattering SM, see Standard Model channel, 86, 87, 88, 92, 93, 94, 95, 96, 137, 138, Sohnius, Martin, 512 143, 574, 575, 581, 602 soliton, 356, 400, 416, 557, 558, 561 deep inelastic, 38, 45, 64, 90, 92, 118, 187, 192, Sommerﬁeld, Charles M., 368 205, 209, 421, 427, 428, 544 Sourlas, Nicolas, 454, 490 diffractive, 124 spinor, see fermion elastic, 85, 94, 96 SSC, 193 matrix, see S-matrix theory SSR, see sum rule, superconvergence unitarity, 70, 84, 91, 92, 98, 143, 144, 574, 575, Standard Model, 18, 100, 275, 323, 386, 407, 577, 578 427–428, 436, 442, 499, 513, 514, 521, 522, scattering amplitude, 105–106 529, 553, 571 analyticity, 84, 87, 92, 93, 574, 575 Stanford Linear Accelerator Center, see SLAC asymptotic behaviour, 93, 95, 97, 98, 583, 584 Stirling approximation, 313, 321 Breit–Wigner, see Breit–Wigner amplitude Stony Brook University, 454 crossing symmetry, 84, 86, 91, 98, 574, 579, 601 Stora, Raymond, 520 Koba–Nielsen, see Koba–Nielsen amplitude strangeness, 88, 89, 90, 570 loop, see loop diagram Strassler, Matthew J., 322 N-point dual, 137–139 Strathdee, John A., 453 planar, 31, 56, 98, 122, 124, 161, 240, 264, 270, string 271, 285, 460 closed, see also model, Shapiro–Virasoro, 97, 141, tree-level, 578 142, 143, 144, 145, 590–597, 624 Schecter, Joe, 370 coupling constant, 424, 453, 462, 467, 469, 623 Scherk, Joel,¨ 6, 14, 45, 47, 49, 51, 52, 65, 66, 73, 74, ﬁeld theory, 322, 370, 411, 463–464, 468, 469, 529, 75, 129, 191, 192, 253, 348, 349, 354, 355, 535, 536 356, 373, 386, 410, 422, 423, 430, 437, 441, length scale, 251 454, 463, 464, 475, 478, 490–491, 492, 493, noncritical, see also Liouville theory, 544–550 496–504, 511, 513, 529, 611 open, see also model, dual resonance, 97, 139, 141, Scherk–Schwarz supersymmetry breaking 142, 143, 144, 590–597, 598, 600, 620 mechanism, see supersymmetry breaking scattering, 597–600 Schmid, Christoph, 8, 95, 393 supersymmetric, see superstring Schwarz, John H., 5, 6, 7, 12, 15, 37–56, 65, 67, 70, tension, 91, 98, 224, 226, 423, 431, 587, 620 74, 75, 129, 192, 196, 197, 199, 200, 255, 256, world-sheet, 97, 135, 136, 139, 141, 142, 149, 150, 289, 332, 338, 348, 349, 350, 354, 355, 357, 221, 222, 229, 230, 434, 438, 443, 518, 519, 369, 374, 375, 386, 387, 422, 423, 430, 441, 556, 563, 587, 588 450, 475, 478, 480, 496–504, 513, 515, 517, string action, see action 523, 525, 529, 531, 532, 534, 536, 538, 555, string revolution, 37, 145, 357, 518, 523, 525–526, 605 536–538, 552, 554–555, 567 Schwimmer, Adam, 23, 27, 185, 215, 238 Strominger, Andrew, 55, 469, 525, 539, 555, 560 Schwinger term, see central extension Sudarshan, Ennackal C. G., 361

Index 635

Sudbery, Antony, 290 SVM, see model, Shapiro–Virasoro Sugawara construction, 344–345, 357, 375, Symanzik, Kurt, 407, 432 398–400 Sugawara, Hirotaka, 344, 362 tachyon, 30, 42, 43, 44, 46, 50, 130, 140, 142, SUGRA, see supergravity 153–155, 163, 170, 175, 199, 209, 237, 253, sum rule 255, 264, 278, 284, 285, 289, 298, 314, 315, Adler–Weisberger, 102, 573 317, 331, 332, 337, 338, 339, 341, 352, 353, finite energy, 22, 39, 95–97, 100, 102–104, 354, 356, 363, 370, 411, 437, 438, 452, 454, 106–108, 110, 119, 157, 173, 194, 204, 277, 460, 497, 501, 502, 529, 531, 534, 581, 594, 474, 528, 576 596, 599, 600, 601, 610, 611, 612, 621 superconvergence, 107, 108, 576 tadpole, 55, 452, 531, 534 super-Virasoro algebra, see superconformal algebra Tamm, Igor Y., 116 Superconducting Super Collider, see SSC tetrad, see vierbein superconformal Theory of Everything, 18, 120, 184, 192, 388, 453, algebra, 43, 337, 339, 376, 382, 383, 453, 480, 552, 600 605–610 Thirring model, 356, 400, 402 symmetry, 44, 46, 342, 396, 443, 501 ’t Hooft, Gerard, 257, 313, 370, 428, 432, 464, 466, supercurrent, 342, 443, 485, 605, 608, 615 468, 477, 529, 545, 546 superfield, 289, 469, 480, 617–618 Thorn, Charles B., 5, 43, 73, 76, 150, 152, 199, 222, supergravity, 49–56, 423, 436, 442, 443, 444–445, 233, 241, 242, 244, 246–249, 250, 253, 288, 454, 468, 480, 486, 501, 504, 512–514, 521, 297, 317, 319, 320, 349, 363, 376, 384, 393, 522–525, 531, 532, 535, 537, 554–555, 556, 447, 479, 531 557, 558 Todorov, Ivan T., 349 supergroup collaboration, see Ademollo et al. TOE, see Theory of Everything collaboration Toller, Marco, 239 superspace, 305, 416, 435, 453, 479, 481, 535, Tomonaga, Sin-Itiro, 281 617–618 topological field theories, 547, 566, 567 superstring, 30, 52–55, 129, 130, 314, 315, 321, 322, torus geometry, 53, 136, 256, 303, 439, 493, 534, 332, 355, 396, 438, 439, 440, 442, 514, 612 515–518, 521–526, 532–536, 554–555, Touschek, Bruno, 172, 173, 174 556–553 trace anomaly, see conformal anomaly dualities, 48, 55, 470, 502, 536, 547, 549, 556–557 Treiman, Sam B., 194 heterotic, 49, 55, 196, 402, 493, 500, 518, 525, 538, Tsou, Sheung T., 214 539, 555, 556, 557, 558, 564 Tyutin, Igor V., 520 type I, 53, 54–55, 513, 515–516, 518, 521, 523, 532, 537, 554, 557 unification, 427–431, 554, 555 type IIA, 51, 53, 503, 513, 515, 516, 518, 521, 523, in field theory, see Grand Unified Theories 532, 534, 554, 557, 558 in string theory, 46–49, 429–431, 464, type IIB, 53, 513, 515–516, 518, 521, 522, 523, 498–501 532, 534, 535, 554, 557 in supergravity, 54, 502, 531, 532, 536 superstring action, see action, superstring unitarity, see scattering supersymmetric partner, see also supersymmetry, Utiyama, Ryoyu, 461, 467 multiplet, 50, 436, 454 supersymmetry, 30, 44, 45, 49–52, 130, 191, 195, 216, Vafa, Cumrun, 560, 567 256, 290, 322, 356, 369, 376, 435, 453, 549, van Nieuwenhuizen, Peter, 445, 454, 502, 552, 553, 560, 564, 567 503 breaking, 52, 441–442, 503–504, 553 Varenna Summer School, 245 extended, 51, 55, 322, 453, 481, 501, 512–513, 533, Veltman, Martinus J. G., 407, 428 554 Veneziano amplitude, 24, 68, 84, 97–99, 113–114, multiplet, 537, 612, 617 119, 136, 137, 140, 149, 160, 194, 198, 240, spacetime, 307, 410, 434–437, 438, 454–456, 476, 262–264, 266, 267, 270, 279, 313, 322, 334, 501–503, 529, 533, 545, 548, 613–618 362, 408, 449, 576, 578, 579, 581, 584, world-sheet, 44, 332, 341–344, 396, 409–410, 434, 602 453, 485–488, 604–610 DHS duality in, 40, 130, 209, 581–582 Susskind, Leonard, 5, 11, 72, 136, 238, 262–264, 272, Regge behaviour of, 583–584 286, 323, 355, 447, 459 spectrum of, 113, 284, 582–583 SUSY, see supersymmetry Veneziano model, see model, dual resonance

636 Index

Veneziano, Gabriele, 4, 8, 9, 17, 23, 33, 40, 64, 97, Weyl, Hermann K. H., 352 100, 108, 135, 148, 149, 173, 191, 198, 204, White, Alan R., 239, 379 214, 215, 221, 236, 237, 262, 267, 283, 284, Wilczek, Frank, 428, 535 287, 313, 334, 336, 346, 560, 561 Willemsen, Jorge F., 280 Verma module, see also conformal representation, Wilson loop, 468, 546, 547, 549 242, 320 Wilson, Kenneth G., 431, 529, 545 vertex Wilson, Robert R., 194, 362, 364, fermionic, 254, 339, 354, 357, 368, 382–389, 478, 368 529 Witten, Edward, 54, 55, 200, 285, 403, 465, 469, 514, N-Reggeon, 145, 170, 198, 215, 319, 339, 362, 523, 524, 525, 533, 535, 537, 539, 547, 548, 460, 463, 492 554, 555, 557, 564, 566, 567 operator, 149, 158, 161, 168, 169, 256, 299, 315, world-sheet, see string world-sheet 318, 357, 365, 395, 400–403, 460, 531, 532, Wray, Dennis, 215 549, 598, 599, 600, 601 WZ model, see Wess–Zumino model vierbein, 442, 444–445, 480, 513 WZWN model, see Wess–Zumino–Witten–Novikov Virasoro model algebra, 27, 147, 149, 166, 242, 247, 249, 352, 358, 380, 381, 394, 398, 400, 409, 415, 520, 563, Yan, Tung-Mow, 431 590, 604 Yang–Mills theory, see gauge theory, non-Abelian amplitude, 40, 141, 142, 491, 528 Yellin, Joel, 181 conditions, 26, 42, 44, 47, 165–168, 185, 232, 237, Yoneya, Tamiaki, 6, 65, 73, 75, 415, 430, 459–470, 241, 251, 317, 320, 383, 384, 387, 448, 497, 500 597 Virasoro, Miguel A., 9, 23, 70, 100, 108, 141, 214, Zakrzewski, Wojtek, 379 347, 363, 373, 376, 393 Zambuto, Mauro, 361 Volkov, Dmitry V., 434 Zamolodchikov, Alexander B., 547, 556, 563, 564, 565 Wadia, Spenta, 467 Zamolodchikov, Alexei B., 565 Waltz, Ron, 243 Zatzkis, Henry, 361 Weinberg, Steven, 38, 100, 255, 355, 386, 407, 427, zero mode, 42, 297, 301, 336, 337, 340, 369, 387, 571 397, 402, 486, 515, 591, 592, 593, 599, 601, Weingarten, Donald H., 363, 364, 374 608, 611 Weis, Joseph H., 9, 27, 166, 242, 322, 352, 358, 393, zero-point energy, see also Casimir, energy, 263, 267, 394 273, 339, 449, 478, 479, 593, 594, 595, Weisberger, William I., 573 609 Weisz, Peter H., 432 zero-slope limit, 47, 348, 375, 410, 423–427, 430, Wentzel, Gregor, 116 462, 463, 464, 466, 467, 469, 475, 486, 493, Wess, Julius, 6, 44, 66, 195, 407, 410, 422, 434, 438, 498, 513, 521, 620–624 475, 501 zero-width approximation, see also resonance Wess–Zumino model, 45, 49, 195, 337, 434–436, width, 130, 204, 209, 313, 314, 316, 613–616, 617, 618 576 Wess–Zumino–Witten model, see Zimmermann, William, 407 Wess–Zumino–Witten–Novikov model Zuber, Jean-Bernard, 564 Wess–Zumino–Witten–Novikov model, 398, 535, Zumino, Bruno, 6, 44, 54, 66, 191, 195, 357, 407, 408, 564, 567 410, 422, 434, 438, 442, 445, 475, 479, 486, Weyl 501, 502, 536 anomaly, see conformal anomaly Zwanziger, Daniel, 407 fermion, see fermion zweibein, see also vierbein, 487 invariance, 306, 519, 589 Zweig, George, 89, 571