Superspace BRST/BV Operators of Superfield Gauge Theories

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 (???). 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 (delta). 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.

Automated summary

This article discusses 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, the nilpotent superspace BRST symmetry transformation is defined. The BV-BRST nilpotent differential operator is constructed using an appropriate set of anti-superfields and the superspace antibracket, expressed in terms of superspace covariant derivatives. The anti-superfield independent terms of the operator provide a superspace generalization of the Koszul-Tate resolution.