Superspace BRST/BV Operators of Superfield Gauge Theories

Abstract

We consider the superspace BRST and BV description of 4D,N=1 super-Maxwell theory and its non-abelian generalization Super Yang–Mills. By fermionizing the superspace gauge transformation of the gauge superfields, we define the nilpotent superspace BRST symmetry transformation (𝓈). After introducing an appropriate set of anti-superfields and defining the superspace antibracket, we use it to construct the BV-BRST nilpotent differential operator (s) in terms of superspace covariant derivatives. The anti-superfield independent terms of s provide a superspace generalization of the Koszul–Tate resolution (δ). In the linearized limit, the set of superspace differential operators that appear in s satisfy a nonlinear algebra which can be used to construct a BRST charge Q, without requiring pure spinor variables. Q acts on the Hilbert space of superfield states, and its cohomology generates the expected superspace equations of motion.