By Olivier Piguet, Klaus Sibold (auth.)
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Extra info for Renormalized Supersymmetry: The Perturbation Theory of N = 1 Supersymmetric Theories in Flat Space-Time
2. BRS - invariance In this section we wish to reformulate gauge invariance as BRS (Becchi-Rouet-Stora)-invariance and in particular to derive the Wardidentity associated with it - the Slavnov-identity. Eventually it will be this latter which defines the theory. Before dOing so let us emphasize again that the BRS-transformations have two aspects which have conceptually nothing to do with each other. The first is that they comprise the algebraic (and geometric) structure of the gauge group - a classical object.
6,8J. Since we shall not use this gauge in higher orders we will not pursue this subject any further. 6J has to comprise the abelian gauge invariant interaction of the photon and the electron with additional fields in order to achieve supersymmetry. Since the partner of the v~ in an abelian gauge superfield - the Weyl spi nor A - is not charged it cannot be i denti fi ed wi th even a part of the electron. Hence other spinors are needed and since the smallest multiplets are chiral ones we use those to provide the spinors.
The mass spectrum is: one ~mplex scalar of mass W, one vector an,d one real scal ar of mass g2a2 , two spinors of mass ~2 + ~2a2 and the massless Goldstone spinor. This case will not be discussed any further. t Returning to case (I) we first wish to re-establish the general gauge. 87) hence none of the conclusions reached before is affected. 87) are not determined which is allright since these fields are subjected to inhomogeneous gauge transformations. e. 92 ) The gauge parameter a itself is fixed by its appearance in the gauge \Jard-identity.
Renormalized Supersymmetry: The Perturbation Theory of N = 1 Supersymmetric Theories in Flat Space-Time by Olivier Piguet, Klaus Sibold (auth.)