Too Beautiful to Ignore Supersymmetry 1970-1976 Pierre Ramond University of Florida Dirac’s 1939 James Scott Prize Lecture on the relation between Mathematics and Physics Experiment and Observation Mathematical Reasoning Newton: Simplicity Einstein: Mathematical Beauty where simplicity and beauty clash … Opt for Beauty! some concepts are too beautiful to ignore: Supersymmetry 1970-1976 1939: Wigner finds two weird massless “Infinite Spin” representations with different helicity strings 5 3 1 1 3 5 , , , , + , + , + , ··· −2 −2 −2 2 2 2 ··· ? , 2, 1, 0, +1, +2, ··· − − ··· Supersymmetry born on both sides of the iron curtain in 1970 5 from 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. 6 π - N scattering resonances Imyfr, Regge pole boson-fermion! 7 Veneziano Model (bosons only) = extract vertex & propagator from amplitudes 8 String Model 1 2 2 L0 = p + oscillators = P P L0 + m · Pµ = pµ + (oscillators)µ ik Q ˙ e · Pµ = Qµ 9 µ Dirac equation γµ p + m =0 Pµ = pµ + (oscillators)µ 10 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) 11 Dirac structure requires anticommuting oscillators with vector indices learned much later that in D=10 space-time dimensions, the little group vector and spinor have the same dimension Mercedes Dynkin diagram! . 12 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 13 Superstring amplitudes Dual Pion Model = fermion boson 14 Dual Pion Model fermion and boson: same theory different boundary conditions 15 long soviet winters, long soviet summers, also lead to supersymmetry 16 Berezin & Kac, 1970 17 Gol’fand & Likhtman, 1971 extension of space-time symmetry 18 posit super-invariant interaction between Wess-Zumino and gauge multiplets (not quite right) nobody notices 19 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” 20 1970 Russians Superstrings 1973 WZ 1976 Sugra MSSM 21 Wess & Zumino, 1973 from the superstring side to four dimensions free scalar and vector supermultiplets with auxiliary fields 22 Wess & Zumino, 1974 one loop structure of WZ multiplet no quadratic divergences Likthman, 1975 only wave function renormalization Källen, 1949 23 CPT 1 1 Super Poincaré Group (λ, λ + ) + ( λ, λ ) 2 − − − 2 Two helicities multiplets Wess-Zumino SuperGauge SuperGravity Gol’fand-Likthman self-conjugate multiplets (Gell-Mann 1974) 1 1 N=4 Super Yang-Mills 1 +4 +6 0 +4 + 1 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 Super Higgs mechanism R-symmetry neutrino as Goldstone fermion 25 1976 Freedman, van Nieuwenhuisen & Ferrara N=1 Supergravity graviton-gravitino interacting theory 26 1976 Brink, Schwarz & Scherk interacting N=4 SuperYang-Mills 27 1976 Gliozzi, Olive & Scherk comes full circle supersymmetric string in ten dimensions 28 1976 Gildener & Weinberg gauge hierarchy 29 1976 Fayet Birth of the Supersymmetric Standard Model two scalar superfields leptons & quarks in WZ multiplets continuous R-symmetry 30 Superstrings still in flight IIA HET M IIB HET’ I 31 Plato’s Cave Coset Physics 32 1931 Blanche Calloway “It Looks like Susie” 33 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 . 34.