SUPERSYMMETRY

BRUNO ZUMINO

LECTURES DELIVERED AT UNIVERSITY OF CALIFORNIA,BERKELEY

WINTER, 1982

Contents

SUPERSYMMETRY = FERMI-BOSE SYMMETRY 1Infinitesmal SUSY transformation, equations of motion, gamma matrix propertiesand Fierz rearrangement, SUSY algebra and charges, Emmy Noether’s theorem,SUSY current

SUPERSPACE AND SUPERFIELDS 13Supercurrents and superfields, Weyl representation of gamma matrices, infinites-mal superfield transformation and superderivatives, chiral superfields, integrationover anti-commuting variables, real superfields

SUPERSPACE LAGRANGIAN FOR W-Z MODEL 25

LAGRANGIAN FOR A VECTOR SUPERMULTIPLET & SUSY QED 27

SUSY YANG MILLS 29Recap of Yang Mills, SUSY Yang Mills, N = 2 and N = 4 matter content andLagrangians

SPONTANEOUS BREAKING OF SUSY 38Fayet-Iliopoulos term, mass sum rules, general theory of chiral superfields, gold-stino, O’Raifeartaigh-Fayet model of spontaneous SUSY breaking, scalar poten-tial for a SUSY gauge theory

FUNCTIONAL METHODS AND RENORMALIZATION 49Feynman rules by functional methods, supergraphs, non-renormalization of massesand scalar self couplings, wave function renormalization

QUANTUM SUPERSYMMETRIC GAUGE THEORIES 57RECAP OF FADDE’EV POPOV GHOSTS . . . . . . . . . . . . . . . . . . . . . . 57GAUGE FIXING IN SUPERSPACE . . . . . . . . . . . . . . . . . . . . . . . . . . 61

Ghost superfields, projection operators, SUSY Feynman gaugePOWER COUNTING AND DEGREE OF DIVERGENCE . . . . . . . . . . . . . . . 67

Example: one-loop corrections to N = 4 SUSY Yang MillsCOLEMAN-WEINBERG FORMULA FOR THE EFFECTIVE ONE-LOOP POTENTIAL 71

Vacuum degeneracy for spontaneously broken susy, mass matrices andsum rules

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