The Birth of (1970-1976)

Pierre Ramond

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

π π

N N

fermion boson

5 Veneziano Model ( only)

=

extract vertex & propagator from amplitudes

6 Model

1 2 2 L0 = p + oscillators = P P L0 + m ·

Pµ = pµ + (oscillators)µ

ik Q ˙ e · Pµ = Qµ

7 µ Dirac equation µ p + m =0

Pµ = pµ + (oscillators)µ

8 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) 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

2-d supersymmetry

11 Superstring

1 2 2 L0 = p + oscillators = P P L0 + m ·

1 F0 = P + m = p + oscillators F0 + m · ·

ik Q e ·

ik Q 5e · (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 (⇣†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”

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 (, + ) + ( , ) 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 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 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

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