Post on 21-May-2020
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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