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 µ p + m =0

Pµ = pµ + (oscillators)µ

10 Generalized Dirac equation

µPµ + m =0

, = ⌘ { µ ⌫ } µ⌫

= + (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 (⇣†µ †µ⇣) ! ! 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 (, + ) + ( , ) 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