DOCSLIB.ORG

© Cambridge University Press Cambridge

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Cambridge University Press 978-0-521-86069-7 - String Theory and M-Theory: A Modern Introduction Katrin Becker, Melanie Becker, and John H. Schwarz Index More information Index acceleration equation, 528 multiloop, 91 action off-shell, 105 p-brane, 7, 19, 23 one-loop, 94 sigma-model form, 29 Shapiro–Virasoro, 91 D0-brane, 149, 185 anomalous dimension, 653, 672 Einstein–Hilbert, 301 BMN operator, 680 in D dimensions, 550 anomaly Einstein–Maxwell, 560 characteristic class, 174, 176, 177 Nambu–Goto, 24, 26, 27, 155 conformal, 62, 66, 76, 658 point-particle, 18 form, 174, 178 nonrelativistic limit, 20 hexagon diagram, 170 Polyakov, 26 inflow mechanism, 183 string sigma-model, 26, 30, 37 M5-brane, 184 cosmological constant term, 28 NS5-brane, 184 supergravity in 11 dimensions, 304 R symmetry, 657, 673, 676 type I supergravity, 318 superconformal, 143 type IIA supergravity, 311 triangle diagram, 170 type IIB supergravity, 314, 317 anomaly cancellation, 9, 421 ADE E8 × E8,179 classification of singularities, 360, 436 SO(16) × SO(16), 292 Dynkin diagrams, 423 11-dimensional supergravity, 181 gauge group, 437 at M-theory boundary, 182 groups, 422, 423 heterotic M-theory, 470 subgroups of SU(2), 437 in six dimensions, 182, 426, 454 adjunction formula, 370 R symmetry, 672 Adler–Bardeen theorem, 170 type I superstring theory, 176 AdS/CFT duality, 15, 330, 612, 638 type IIB superstring theory, 175 for D3-branes, 638, 642 anthropic principle, 522 for half-BPS states, 654 anthropic reasoning, 15, 522 for M2-branes, 643 anti-de Sitter space, 15, 375, 377, 612 for M5-branes, 644 D = 4, 351 affine connection, 445 D = 5, 494 affine Lie algebra, 68 boundary-operator renormalization, 653 Aharanov–Bohm effect, 198 conformal equivalence class, 652 Aichelburg–Sexl metric, 633 covering space, 646 almost complex structure, 448, 466 Euclideanized, 647, 651 amplitude Feynman rules, 652 N tachyon, 91 global coordinates, 647, 686 absence of UV divergence, 83 in (d + 1) dimensions, 616 D0-brane scattering, 630 nonnormalizable modes, 654 in GS formalism, 148 normalizable modes, 654 large-N gauge-theory, 641 path integral, 651 M-theory, 632 Penrose diagram, 646 726 © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-86069-7 - String Theory and M-Theory: A Modern Introduction Katrin Becker, Melanie Becker, and John H. Schwarz Index More information Index 727 Poincar´e coordinates, 645, 646, 686 extremal for D =5,559 antibrane, 211 temperature of, 565 anticommutation relations rotating and BPS for D = 5, 573 fermionic oscillators, 124, 164 Schwarzschild, 552, 554 heterotic string fermions, 256 in D dimensions, 553 world-sheet fermion fields, 120 supermassive, 549 area law, 661, 662 temperature of, 562 attractor equation, 590, 593 thermodynamic properties, 14, 562 attractor mechanism, 587 black ring, 596, 608 auxiliary field blow-up, 367, 368, 373, 435, 455 in point-particle action, 19, 22, 145, 185 BMN limit, 680 in world-sheet supermultiplet, 113–115 BMN operator, 680 PST, 314 anomalous dimension, 680 world-sheet metric, 7, 26, 27, 31 correlation function, 681 axion, 316, 401, 492, 498, 541 Born–Infeld action, 231, 246, 687 axion–dilaton field, 316, 476, 481, 484, 485, bosonic ghost fields, 142 524 bosonic string, 17 number operator, 43 background fields, 81, 89, 227, 228, 230, 237, bosonization, 67 267, 275, 281, 295, 628, 629 of ghosts, 80 NS–NS, 227, 237, 245 bound state R–R, 229, 237 of D0-branes, 331, 626 background-field gauge condition, 627 of strings, 328 Bekenstein–Hawking entropy formula, 14, 563, threshold, 331 603, 609, 648 boundary condition leading correction to, 585 Dirichlet, 33, 164, 187, 193–195, 201, 202, Beltrami differential, 92 210, 622, 623 Bertotti–Robinson metric, 562 Neumann, 164, 202, 209 Betti numbers, 363, 442 boundary state, 171 SN of , 443 BPS Bianchi identity (p, q) string, 327 for antisymmetric tensor field, 245 bound, 151, 297, 300, 353, 408, 485, 655 for four-form in heterotic M-theory, 521 D-string, 325 for Maxwell field, 560 branes, 296, 421 for Riemann tensor, 384 tensions, 307, 341 with H flux, 511, 516 D-branes, 208, 209, 213, 228, 230, 621, 638 with D3-brane source, 483, 492 type IIA, 405 with M5-brane source, 353 Big Bang, 16 type IIB, 328, 405 biholomorphic function, 61 F-string, 221 Birkhoff’s theorem, 552 M-branes, 307, 332, 614 black p-branes, 14, 551, 613 M-theory solutions, 617 nonextremal, 625 states, 298, 328, 408 black D-branes in nine dimensions, 340 nonextremal, 686 wrapped D-branes, 414 black holes, 14, 408, 549 tensions, 427 challenges posed by, 550 brane–antibrane annihilation, 212, 587 dyonic, 590 brane–antibrane inflation, 537, 540 entropy of, 14, 563, 570, 604 brane–brane inflation, 539 extremal, 558 brane-world scenario, 11, 354, 459, 493 with four charges for D = 4, 574 Brink–Schwarz superparticle, 185 with three charges for D = 5, 567 BRST inner and outer horizons, 557 charge, 77 multi-center solutions, 594 for RNS string, 143 nonextremal, 572 mode expansion, 77 D = 4, 581 nilpotency, 78, 107 D = 5, 586 cohomology, 79, 108 production at accelerators, 552 quantization, 75, 108 Reissner–Nordstr¨om, 557 symmetry, 77 entropy of, 564 of RNS string, 142 extremal, 558 bubbling AdS, 655 © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-86069-7 - String Theory and M-Theory: A Modern Introduction Katrin Becker, Melanie Becker, and John H. Schwarz Index More information 728 Index Calabi–Yau four-fold, 458, 460–463, 466, 467, chiral fields, 170, 174 469, 471, 477, 478, 547, 548 of type I theory, 176 elliptically fibered, 475 of type IIB theory, 175 examples, 476 on an M5-brane, 184 Hodge numbers, 473 self-dual tensor, 172, 175 holomorphich four-form, 474 Weyl fermion, 174 K¨ahler form, 473 Weyl gravitino, 175 Calabi–Yau manifold, 5, 10, 356 chiral matter, 417 n-folds, 363 chiral primary operator, 656, 672 mirror symmetry, 10 chiral superfield, 666 one-folds, 366 chiral supermultiplet, 417, 473 two-folds, 366 chiral-symmetry breaking, 611 Calabi–Yau three-fold, 588 chirality, 134, 302 conifold singularity, 488 in ten dimensions, 136 elliptic fibration, 455 of dilatino, 137 Euler characteristic, 365 of gravitino, 137 heterotic string compactification, 415 of R sector, 136 Hodge diamond, 364 of type IIB theory, 136 intersection numbers of Weyl spinor, 134 of three-cycles, 392 projection operators, 134 K¨ahler form, 381 Christoffel connection, 23, 384, 509, 510, 513, M-theory compactification, 401, 410 517, 547 metric deformations, 388 Clifford algebra, 110, 166, 299 product structure of moduli space, 391 closed form, 442 quintic, 370 closed string, 32 supersymmetric three-cycle, 409 closed time-like curve, 359, 551, 645 special Lagrangian submanifold, 405 CMB anisotropy, 531 three-torus fibration, 414 cocycle, 67 type IIA compactification, 400, 402 cohomology, 79, 441 type IIB compactification, 400, 402, 403, BRST, 79, 87, 105, 108, 144 408, 588 classes, 79, 211, 321, 395, 589 volume form, 384 constraint, 416 calibration, 435, 439 de Rham, 442, 467 canonical homology basis, 590 canonical momentum, 35 Dolbeault, 449 Cartan matrix of Calabi–Yau four-fold, 474, 500 of Calabi–Yau three-fold, 392 E8, 294 SU(3), 285 of K3, 419 Casimir invariants of Riemann surface, 95 of SU(N), 657, 669 primitive, 467–469 central charge, 42, 62, 297, 300 cold dark matter, 531 central extension, 42, 57, 62 commutation relations, 55 Chan–Paton Kac–Moody algebra, 69 charges, 101, 196, 197, 222, 244, 250 of bosonic oscillators, 124 factors, 196 Poincar´e algebra, 56 index, 197 compactification, 5 matrix, 197, 198 F-theory chaotic inflation, 534 on K3, 427, 433 characteristic class, 157, 172–174 heterotic string factorization, 180 on a Calabi–Yau three-fold, 357, 374, 387, charge-conjugation matrix, 153 415, 418 Chern character, 174 on a three-torus, 420 factorization property, 177 with flux, 508 Chern class, 471 M-theory first, 363, 370, 371, 382, 451, 453 on a G2 manifold, 433, 434, 436 second, 186 on a Spin(7) manifold, 438 Chern–Simons form, 157, 174, 179, 186 on a Calabi–Yau four-fold, 461, 499 Chern–Simons term on a Calabi–Yau three-fold, 401, 405, 410 D7-brane, 483 on K3, 419, 423 in five dimensions, 658 with conical singularity, 436 chiral algebra, 71 on a circle, 188, 190, 193, 198, 199, 202, 209, © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-86069-7 - String Theory and M-Theory: A Modern Introduction Katrin Becker, Melanie Becker, and John H. Schwarz Index More information Index 729 211, 214, 234, 244, 271, 329, 330, 333, infinitesimal, 61, 74 337, 339 special, 60, 62 toroidal, 265, 266, 268, 270, 274, 275, 278, conical singularity, 360, 670 280, 287, 288, 291, 340, 345, 397 conifold, 354, 487–489, 669, 671, 675, 684, 687 type IIA superstring deformed, 488, 490, 496, 498, 673, 675, 684 on a Calabi–Yau three-fold, 400, 402 with wrapped D6-branes, 685 on K3, 424–426 geometry, 489, 491 type IIB superstring isometry group, 489 on a Calabi–Yau three-fold, 400, 402, 403, K¨ahler form, 548 408, 498, 502 resolved, 488, 490, 684 on K3, 426, 454 with wrapped D5-branes, 685 with flux, 480 singularity, 403, 404, 454, 487, 488, 490, 497 warped, 355, 456 transition, 357, 385, 403, 487, 685 with branes, 376 warped, 492, 674 with flux, 13, 458 with fluxes, 491 complex geometry, 449 coordinate singularity, 554, 559 complex projective space, 369, 453 correlation functions, 73 Fubini–Study metric, 369 generating function, 652 K¨ahler potential, 369 coset-space theory, 69 complex structure, 90, 448, 513 cosmic censorship conjecture, 550, 551, 558 deformations, 370, 388, 391 cosmic
Recommended publications
  • Arxiv:Math/0406039V3

    Arxiv:Math/0406039V3

    CURVATURE OF MULTIPLY WARPED PRODUCTS FERNANDO DOBARRO AND BULENT¨ UNAL¨ Abstract. In this paper, we study Ricci-flat and Einstein Lorentzian multiply warped products. We also consider the case of having constant scalar curvatures for this class of warped products. Finally, after we introduce a new class of space- times called as generalized Kasner space-times, we apply our results to this kind of space-times as well as other relativistic space-times, i.e., Reissner-Nordstr¨om, Kasner space-times, Ba˜nados-Teitelboim-Zanelli and de Sitter Black hole solutions. Contents 1. Introduction 2. Preliminaries 3. Special Multiply Warped Products 3.1. Einstein Ricci Tensor 3.2. Constant Scalar Curvature 4. Generalized Kasner Space-time 5. 4-Dimensional Space-time Models 5.1. Type (I) 5.2. Type (II) 5.3. Type (III) 6. BTZ (2 + 1)-Black Hole Solutions 7. Conclusions References arXiv:math/0406039v3 [math.DG] 11 Dec 2004 Date: October 26, 2004. 1991 Mathematics Subject Classification. 53C25, 53C50. Key words and phrases. Warped products, Ricci tensor, scalar curvature, Einstein manifolds. Research of F. D. partially supported by funds of the National Group ’Analisi Reale’ of the Italian Ministry of University and Scientific Research at the University of Trieste. 1 2 FERNANDODOBARROANDBULENT¨ UNAL¨ 1. Introduction The concept of warped products was first introduced by Bishop and O’Neill (see [20]) to construct examples of Riemannian manifolds with negative curvature. In Riemannian geometry, warped product manifolds and their generic forms have been used to construct new examples with interesting curvature properties since then (see [19, 20, 24, 27, 32, 40, 41, 52, 53, 54, 57, 60]).
  • Abdus Salam United Nations Educational, Scientific and Cultural XA9952968 Organization International Centre

    Abdus Salam United Nations Educational, Scientific and Cultural XA9952968 Organization International Centre

    the IC/99/74 abdus salam united nations educational, scientific and cultural XA9952968 organization international centre international atomic energy agency for theoretical physics D = 4 YANG-MILLS CORRELATORS 5 FROM NSR STRINGS ON AdS5 x S Dimitri Polyakov 30-47 Available at: http://www.ictp.trieste.it/~pub-off IC/99/74 United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS D = 4 YANG-MILLS CORRELATORS 5 FROM NSR STRINGS ON AdS5 x S Dimitri Polyakov^ The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy. Abstract In our previous work (hep-th/9812044) we have proposed the sigma-model action, conjectured to be the NSR analogue of superstring theory on AdS$ x S5. This sigma- model is the NSR superstring action with potential term corresponding to the exotic 5- form vertex operator (branelike state). This 5-form potential plays the role of cosmological term, effectively curving the flat space-time geometry to that of AdS$ x S5. In this paper we study this ansatz in more detail and provide the derivation of the correlators of the four- dimensional super Yang-Mills theory from the above mentioned sigma-model. In particular, we show that the correlation function of two dilaton vertex operators in such a model reproduces the well-known result for the two-point function in N = 4 four-dimensional 2 2 super Yang-Mills theory: < F (x)F (y) >~ \JLy\» • MIRAMARE - TRIESTE July 1999 E-mail: [email protected] Introduction One of the most profound questions with regard to critical superstring theory in ten dimensions is its relation to our four-dimensional world.
  • Brane Effective Actions, Kappa-Symmetry and Applications

    Brane Effective Actions, Kappa-Symmetry and Applications

    Living Rev. Relativity, 15, (2012), 3 LIVINGREVIEWS http://www.livingreviews.org/lrr-2012-3 in relativity Brane Effective Actions, Kappa-Symmetry and Applications Joan Sim´on School of Mathematics, The University of Edinburgh, and Maxwell Institute for Mathematical Sciences Edinburgh EH9 3JZ, U.K. email: [email protected] Accepted on 9 January 2012 Published on 27 February 2012 Abstract This is a review on brane effective actions, their symmetries and some of their applications. Its first part covers the Green{Schwarz formulation of single M- and D-brane effective actions focusing on kinematical aspects: the identification of their degrees of freedom, the importance of world volume diffeomorphisms and kappa symmetry to achieve manifest spacetime covari- ance and supersymmetry, and the explicit construction of such actions in arbitrary on-shell supergravity backgrounds. Its second part deals with applications. First, the use of kappa symmetry to determine supersymmetric world volume solitons. This includes their explicit construction in flat and curved backgrounds, their interpretation as Bogomol'nyi{Prasad–Sommerfield (BPS) states carrying (topological) charges in the supersymmetry algebra and the connection between su- persymmetry and Hamiltonian BPS bounds. When available, I emphasise the use of these solitons as constituents in microscopic models of black holes. Second, the use of probe approx- imations to infer about the non-trivial dynamics of strongly-coupled gauge theories using the anti de Sitter/conformal field theory (AdS/CFT) correspondence. This includes expectation values of Wilson loop operators, spectrum information and the general use of D-brane probes to approximate the dynamics of systems with small number of degrees of freedom interacting with larger systems allowing a dual gravitational description.
  • Introduction to Path Integral Methods in String Theory

    Introduction to Path Integral Methods in String Theory

    Introduction to path integral methods in string theory Sergio Ernesto Aguilar Guti´errez1 1Instituto de F´ısica Te´orica, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz 271, 01140-070 S~aoPaulo, SP, Brazil∗ (Dated: November 30, 2018) Contents I. Introduction 1 II. Functional methods in bosonic string theory 2 A. Polyakov action 2 B. Symmetries 3 C. Equations of motion and boundary conditions 4 D. Polyakov path integral 6 E. BRST quantization 10 F. Representation theory 11 III. Functional methods in the RNS formalism 12 A. Superstring theory in the RNS formalism 12 B. R and NS sectors 14 C. Local symmetries of the action 16 D. Path integrals in RNS 17 References 19 I. INTRODUCTION The fundamentals of path integral methods in string theory are reviewed with emphasis in the development of the Faddeev Popov ghost that emerge from overcounting of configurations and the conditions that the string theory requires for maintaining Weyl invariance. Since the lecture is presented for a course that does not assume previous knowledge in string theory, I include an introduction to both bosonic and superstring theory (in the RNS formalism). This text begins with an introduction to bosonic string theory, we study the symmetries of the Polyakov action, we work out the canonical quantization of the theory to calculate its central charge. Later the path integral formulation is introduced with the appearance of Faddeev-Popov ghosts, we consider their canonical quantization for computing the central charge. The total central charge generates an anomaly in the Weyl invariance of the theory. The vanishing of such term has powerful implications that yield conditions related with the possible physical states and the dimensions of the theory.
  • Introduction to Superstring Theory

    Introduction to Superstring Theory

    Introduction to Superstring Theory Carmen N´u~nez IAFE (UBA-CONICET) & PHYSICS DEPT. (University of Buenos Aires) VI ICTP LASS 2015 Mexico, 26 October- 6 November 2015 . Programme Class 1: The classical fermionic string Class 2: The quantized fermionic string Class 3: Partition Function Class 4: Interactions . Outline Class 1: The classical fermionic string The action and its symmetries Gauge fixing and constraints Equations of motion and boundary conditions Oscillator expansions . The spectra of bosonic strings contain a tachyon ! it might indicate the vacuum has been incorrectly identified. The mass squared of a particle T is the quadratic term in the 2 @2V (T ) j − 4 ) action: M = @T 2 T =0 = α0 = we are expanding around a maximum of V . If there is some other stable vacuum, this is not an actual inconsistency. Why superstrings? . The mass squared of a particle T is the quadratic term in the 2 @2V (T ) j − 4 ) action: M = @T 2 T =0 = α0 = we are expanding around a maximum of V . If there is some other stable vacuum, this is not an actual inconsistency. Why superstrings? The spectra of bosonic strings contain a tachyon ! it might indicate the vacuum has been incorrectly identified. If there is some other stable vacuum, this is not an actual inconsistency. Why superstrings? The spectra of bosonic strings contain a tachyon ! it might indicate the vacuum has been incorrectly identified. The mass squared of a particle T is the quadratic term in the 2 @2V (T ) j − 4 ) action: M = @T 2 T =0 = α0 = we are expanding around a maximum of V .
  • String Theory and M-Theory: a Modern Introduction Katrin Becker, Melanie Becker, and John H

    String Theory and M-Theory: a Modern Introduction Katrin Becker, Melanie Becker, and John H

    Cambridge University Press 978-0-521-86069-7 - String Theory and M-Theory: A Modern Introduction Katrin Becker, Melanie Becker, and John H. Schwarz Frontmatter More information STRING THEORY AND M-THEORY A MODERN INTRODUCTION String theory is one of the most exciting and challenging areas of modern theoretical physics. This book guides the reader from the basics of string theory to very recent developments at the frontier of string theory research. The book begins with the basics of perturbative string theory, world-sheet supersymmetry, space-time supersymmetry, conformal field theory and the heterotic string, and moves on to describe modern developments, including D-branes, string dualities and M-theory. It then covers string geometry (including Calabi–Yau compactifications) and flux compactifications, and applications to cosmology and particle physics. One chapter is dedicated to black holes in string theory and M-theory, and the microscopic origin of black-hole entropy. The book concludes by presenting matrix theory, AdS/CFT duality and its generalizations. This book is ideal for graduate students studying modern string theory, and it will make an excellent textbook for a 1-year course on string theory. It will also be useful for researchers interested in learning about developments in modern string theory. The book contains about 120 solved exercises, as well as about 200 homework problems, solutions of which are available for lecturers on a pass- word protected website at www.cambridge.org/9780521860697. K ATRIN B ECKER is a Professor of physics at Texas A & M University. She was awarded the Radcliffe Fellowship from Harvard University in 2006 and received the Alfred Sloan Fellowship in 2003.
  • Heterotic String Theory on Calabi-Yau - Manifolds in the Green-Schwarz Formalism*

    Heterotic String Theory on Calabi-Yau - Manifolds in the Green-Schwarz Formalism*

    1 . SLAC - PUB - 4071 August 1986 -. T HETEROTIC STRING THEORY ON CALABI-YAU - MANIFOLDS IN THE GREEN-SCHWARZ FORMALISM* ASHOKE SEN Stanford Linear Accelerator Center - Stanford University, Stanford, California, 94305 ABSTRACT The a-model describing the propagation of the heterotic string in a Calabi- Yau background is written down in the Green-Schwarz formulation. This model has manifest N=l space-time supersymmetry, however only the SO(2) subgroup - of the four dimensional Lorentz group is realized linearly. The criteria for the existence of the full SO(3,l) L orentz symmetry in this model are studied. These requirements turn out to be identical to those obtained by demanding the exis- =- tence of space-time supersymmetry in the Neveu-Schwarz-Ramond formulation - of the theory, where the SO(3,l) L orentz symmetry is manifest, but space-time supersymmetry is not. The analysis is easily generalized to more general back- grounds, which give rise to (2,0) su p erconformal field theories on the world sheet. Finally it is shown that if the requirements which give unbroken N=l space-time supersymmetry and full SO(3,l) L orentz invariance are satisfied, then the unbro- ken gauge group after the compactification of the &3 x J?& heterotic string theory on Calabi-Yau spaces iS Es X Es. - Submitted to Nuclear Physics B * Work supported by the Department of Energy, contract DE - AC03 - 76SF00515. 1. INTRODUCTION Current interest in string theories has its origin at the discovery of anomaly cancellation,[ll subsequent discovery of the heterotic string theory, 121and the -- - semi-realistic compactification of this theory on Calabi-Yau manifolds PI and orbifolds.
  • Brane Effective Actions, Kappa-Symmetry and Applications

    Brane Effective Actions, Kappa-Symmetry and Applications

    Brane Effective Actions, Kappa-Symmetry and Applications Joan Sim´on School of Mathematics and Maxwell Institute for Mathematical Sciences email: [email protected] Abstract This is a review on brane effective actions, their symmetries and some of its applications. Its first part uncovers the Green-Schwarz formulation of single M- and D-brane effective actions focusing on kinematical aspects : the identification of their degrees of freedom, the importance of world volume diffeomorphisms and kappa symmetry, to achieve manifest spacetime covari- ance and supersymmetry, and the explicit construction of such actions in arbitrary on-shell supergravity backgrounds. Its second part deals with applications. First, the use of kappa symmetry to determine supersymmetric world volume solitons. This includes their explicit construction in flat and curved backgrounds, their interpretation as BPS states carrying (topological) charges in the supersymmetry algebra and the connection between supersymmetry and hamiltonian BPS bounds. When available, I emphasise the use of these solitons as constituents in microscopic models of black holes. Second, the use of probe approximations to infer about non-trivial dynamics of strongly coupled gauge theories using the AdS/CFT correspondence. This in- cludes expectation values of Wilson loop operators, spectrum information and the general use of D-brane probes to approximate the dynamics of systems with small number of degrees of freedom interacting with larger systems allowing a dual gravitational description. Its final part briefly discusses effective actions for N D-branes and M2-branes. This in- cludes both SYM theories, their higher order corrections and partial results in covariantising these couplings to curved backgrounds, and the more recent supersymmetric Chern-Simons matter theories describing M2-branes using field theory, brane constructions and 3-algebra considerations.
  • Arxiv:Hep-Th/9804051V1 7 Apr 1998 Ok Ipeagrtmi Ie O Osrcigtecompo G the Are in Constructing Examples Membrane Three for the Given Discussed

    Arxiv:Hep-Th/9804051V1 7 Apr 1998 Ok Ipeagrtmi Ie O Osrcigtecompo G the Are in Constructing Examples Membrane Three for the Given Discussed

    KCL-MTH-98-10 CTP TAMU-11/98 hep-th/9804051 On Brane Actions and Superembeddings P.S. Howe 1, O. Raetzel 1 and E. Sezgin 2† 1 Department of Mathematics, King’s College, London, UK 2 Center for Theoretical Physics, Texas A&M University, College Station, TX 77843, USA Abstract Actions for branes, with or without worldsurface gauge fields, are discussed in a unified frame- work. A simple algorithm is given for constructing the component Green-Schwarz actions. Superspace actions are also discussed. Three examples are given to illustrate the general pro- cedure: the membrane in D = 11 and the D2-brane, which both have on-shell worldsurface supermultiplets, and the membrane in D = 4, which has an off-shell multiplet. arXiv:hep-th/9804051v1 7 Apr 1998 † Research supported in part by NSF Grant PHY-9722090 1 Introduction In the superembedding approach to supersymmetric extended objects the object under consid- eration is described mathematically as a subsupermanifold (the worldsurface) of superspacetime (the target supermanifold). This approach was initiated some time ago [1, 2] in the context of superparticles. Superspace actions were found for particles in D = 3, 4, 6 and 10 dimensional spacetimes [1, 2, 3, 4, 5, 6] and then later for the heterotic string in ten dimensions [7, 8]. Ac- tions of the heterotic string type were constructed for other type I branes (i.e. branes with no worldsurface vector or tensor fields) [9, 10] but it was not clear at the time that these actions described the right degrees of freedom. In [11] a generalised action was proposed for type I branes which leads to the standard Green-Schwarz equations of motion (see [12, 13] for reviews) and this approach has recently been extended to cover D-branes [14, 15, 16].
  • The Ads5 × S5 Superstring

    The Ads5 × S5 Superstring

    CALT-TH-2020-004 5 The AdS5 S Superstring × John H. Schwarz1 Walter Burke Institute for Theoretical Physics California Institute of Technology 452-48 Pasadena, CA 91125, USA Abstract 5 The duality between the type IIB superstring theory in an AdS5 S back- × ground with N units of five-form flux and = 4 super Yang–Mills theory with a N U(N) gauge group has been studied extensively. My version of the construction of the superstring world-sheet action is reviewed here. This paper is dedicated to Michael Duff on the occasion of his 70th birthday. arXiv:2004.09661v2 [hep-th] 22 Jul 2020 [email protected] 1 Introduction I am pleased to contribute to this volume honoring my good friend Michael Duff on the occasion of his 70th birthday. Although we never collaborated, we have had lively scientific discussions, and each of us has influenced the other’s research. In the early 1980s, when Michael Green and I were developing superstring theory, extra dimensions were not yet fashionable. However, this began to change as a result of the work of Michael Duff and his collaborators exploring compactifications of 11-dimensional supergravity [1]. This work attracted a community of followers who acquired expertise that would prove useful in the subsequent development of superstring theory and M theory. Superstring theory was originally developed for a Minkowski spacetime geometry. (For reviews see [2][3][4].) This is the easiest case to handle mathematically, but it is not the only possibility. In particular, there is great interest in Anti de Sitter (AdS) geometries for studies of AdS/CFT duality.

  • Brane Effective Actions, Kappa-Symmetry and Applications

    Edinburgh Research Explorer Brane effective actions, kappa-symmetry and applications Citation for published version: Simon Soler, J 2012, 'Brane effective actions, kappa-symmetry and applications', Living Reviews in Relativity, vol. 15, no. n/a, 3. https://doi.org/10.12942/lrr-2012-3 Digital Object Identifier (DOI): 10.12942/lrr-2012-3 Link: Link to publication record in Edinburgh Research Explorer Document Version: Publisher's PDF, also known as Version of record Published In: Living Reviews in Relativity General rights Copyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy The University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorer content complies with UK legislation. If you believe that the public display of this file breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Download date: 04. Oct. 2021 Living Rev. Relativity, 15, (2012), 3 LIVINGREVIEWS http://www.livingreviews.org/lrr-2012-3 in relativity Brane Effective Actions, Kappa-Symmetry and Applications Joan Sim´on School of Mathematics, The University of Edinburgh, and Maxwell Institute for Mathematical Sciences Edinburgh EH9 3JZ, U.K. email: [email protected] Accepted on 9 January 2012 Published on 27 February 2012 Abstract This is a review on brane effective actions, their symmetries and some of their applications.
  • The Ads₅ X S⁵ Superstring

    The Ads₅ X S⁵ Superstring

    CALT-TH-2020-004 5 The AdS5 S Superstring × John H. Schwarz1 Walter Burke Institute for Theoretical Physics California Institute of Technology 452-48 Pasadena, CA 91125, USA Abstract 5 The duality between the type IIB superstring theory in an AdS5 S back- × ground with N units of five-form flux and = 4 super Yang–Mills theory with a N U(N) gauge group has been studied extensively. My version of the construction of the superstring world-sheet action is reviewed here. This paper is dedicated to Michael Duff on the occasion of his 70th birthday. arXiv:2004.09661v1 [hep-th] 20 Apr 2020 [email protected] 1 Introduction I am pleased to contribute to this volume honoring my good friend Michael Duff on the occasion of his 70th birthday. Although we never collaborated, we have had lively scientific discussions, and each of us has influenced the other’s research. In the early 1980s, when Michael Green and I were developing superstring theory, extra dimensions were not yet fashionable. However, this began to change as a result of the work of Michael Duff and his collaborators exploring compactifications of 11-dimensional supergravity [1]. This work attracted a community of followers who acquired expertise that would prove useful in the subsequent development of superstring theory and M theory. Superstring theory was originally developed for a Minkowski spacetime geometry. (For reviews see [2][3][4].) This is the easiest case to handle mathematically, but it is not the only possibility. In particular, there is great interest in Anti de Sitter (AdS) geometries for studies of AdS/CFT duality.