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Pierre Ramond University of Florida The Birth of Supersymmetry (1970-1976) Pierre Ramond University of Florida still alive 1 Supersymmetry born on both sides of the iron curtain 2 in the west S-Matrix to Superstrings PREDICTION OF REGC}E PARAMETERSIOF p POLES FROM L.oW-ENERGY rN DATA* R. Dolen, D. Hornrf and C. Schmid Callfornta Inatltute of Technologr, Paaadens, Callfornla (Received 23 June 1967) Uslng flnlte-etrerry sum rulea we predlct lmportint features of the Regge structuxe of p polee from low-enerry rN data. The comblned effect of N* resonanrces in generatlng (via the sum rules) propertles of the anolunged p polee ls disoussed, thus startlng a neur type of bootetrap caloulation. 3 π - N scattering resonances Imyfr, Regge pole 4 π - N scattering boson π π fermion N N fermion boson 5 Veneziano Model (bosons only) = extract vertex & propagator from amplitudes 6 String Model 1 2 2 L0 = p + oscillators = P P L0 + m · Pµ = pµ + (oscillators)µ ik Q ˙ e · Pµ = Qµ 7 µ Dirac equation γµ p + m =0 Pµ = pµ + (oscillators)µ 8 Generalized Dirac equation ΓµPµ + m =0 Γ , Γ = ⌘ { µ ⌫ } µ⌫ γ Γ = γ + γ (oscillators) µ ! µ µ 5 µ “The α’s are new dynamical variables which it is necessary to introduce in order to satisfy the conditions of the problem. They may be regarded as describing some internal motion of the electron. …. We shall call them the spin variables.” (Dirac) 9 Dirac structure requires anticommuting oscillators with vector indices!!!! Spin-Statistics? learned much later that in D=10 space-time dimensions, the little group vector and spinor have the same dimension Mercedes-Benz Dynkin diagram! . 10 new kind of symmetry (square root of the Virasoro algebra) F ,F =2L [ L ,F ]=(2m n)F { n m } n+m n m − m+n [ L ,L ]=(m n)L n m − m+n Ln generate the (2-d conformal) Virasoro algebra Fn generate 2-d superconformal algebra 2-d supersymmetry 11 Superstring 1 2 2 L0 = p + oscillators = P P L0 + m · 1 F0 = Γ P + m = γ p + oscillators F0 + m · · ik Q e · ik Q Γ5e · (Neveu & Schwarz) 12 Superstring amplitudes Dual Pion Model = fermion boson 13 Dual Pion Model fermion and boson sectors: supergauges different boundary condition 14 long russian winters, long soviet summers, lead to supersymmetry 15 Berezin & Kac, 1970 16 Gol’fand & Likhtman, 1971 extension of space-time symmetries! 17 write invariant interaction between (Wess-Zumino) and gauge supermultiplets (not totally correct) 18 Volkov & Akulov, 1972 neutrino as a Nambu-Goldstone particle a 0 = + ⇣ xµ x0 (⇣†σµ †σµ⇣) ! ! µ − 2i − nonlinear super σ-model “ … if we introduce gauge fields corresponding to the(se) transformations, then as a consequence of the Higgs effect, a massive gauge field with spin 3/2 arises and the Goldstone particle with spin 1/2 vanishes” 19 1970 Russians Superstrings 1973 WZ 1976 20 Wess & Zumino, 1973 from the superstring side to four dimensions scalar and vector supermultiplets with auxiliary fields no interactions 21 Wess & Zumino, 1974 one loop structure of WZ multiplet no quadratic divergences Likthman, 1975 only wave function renormalization Källen, 1949 22 Fields and the Super Poincaré Group 1 1 (λ, λ + ) + ( λ, λ ) 2 − − − 2 CPT 1 1 Wess-Zumino multiplet + 0 + 0 + (Gol’fand&Likthman) 2 − 2 ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ 1 1 SuperGauge multiplet 1 + + + 1 2 − 2 − ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ 3 3 SuperGravity multiplet 2 + + + 2 2 − 2 − ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ 23 Gell-Mann 1974 self-conjugate multiplets 1 1 1 +4 +6 0 +4 + 1 N=4 Super Yang-Mills 2 − 2 − ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ N=8 SuperGravity 3 1 1 3 2 +8 + 28 1 + 56 + 70 0 + 56 + 28 1 +8 + 2 2 2 − 2 − − 2 − ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ ⇣ ⌘ 24 Fayet 1974 SuSy Higgs mechanism R-symmetry neutrino as Goldstone fermion! 25 1976 Ferrara, Freedman & van Nieuwenhuisen N=1 Supergravity graviton and gravitino Super Einstein tour de force! 26 1976 Brink, Schwarz & Scherk N=4 SuperYang-Mills 27 1976 Gliozzi & Olive & Scherk It all comes together superstring states are space-time supersymmetric (in ten dimensions) 28 1976 Gildener & Weinberg gauge hierarchy paper 29 1976 Fayet Birth of the Supersymmetric Standard Model require two scalar superfields leptons & quarks in WZ multiplets continuous R-symmetry 30 1970 Russians Superstrings 1973 WZ 1976 Sugra MSSM 31 Superstrings still in flight IIA HET M IIB HET’ I 32 Plato’s Cave Coset Physics 33 paraphrasing Dirac Supersymmetry is too beautiful to ignore 34 1931 Blanche Calloway “It Looks like Susie” 35 It looks like Susie It must be Susie I’m sure it’s Susie But I don’t know Could be Virginia With her eyes of Blue Could be Mary Sweet MaryLou But it looks like Susy She talks like Susy She walks like Susy . 36 early hint: Wigner, 1939 Representations of the Poincaré Group massless particle representations with fixed helicity λ p momentum energy E = cp 1 3 5 0, , 1, , 2, , � helicity ±2 ± ±2 ± ±2 ··· the familiar particles 37 Wigner: massless “Infinite Spin” representations with different helicity strings p momentum energy E = cp 5 3 1 1 3 5 , , , , + , + , + , � helicity string ··· −2 −2 −2 2 2 2 ··· ? helicity string , 2, 1, 0, +1, +2, � ··· − − ··· not found in Nature 38.
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