Superspace BRST/BV operators of superfield gauge theories

TL;DR

This paper develops a superspace BRST and BV formalism for 4D, N=1 super Maxwell and super Yang-Mills theories, introducing new operators and algebraic structures to analyze gauge symmetries and equations of motion.

Contribution

It constructs a superspace BRST/BV framework for superfield gauge theories, including a superspace generalization of the Koszul-Tate resolution and a nonlinear algebra for BRST charge construction.

Findings

Defined nilpotent superspace BRST symmetry ($ extstyle extbf{s}$).

Constructed the BV-BRST operator ($ extstylerak{s}$) in superspace.

Derived a superspace algebra for differential operators used to build the BRST charge.

Abstract

We consider the superspace BRST and BV description of $4D,~\mathcal{N}=1$ 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 ($\mathscr{s}$). After introducing an appropriate set of anti-superfields and define the superspace antibracket, we use it to construct the BV-BRST nilpotent differential operator ($\mathfrak{s}$) in terms of superspace covariant derivatives. The anti-superfield independent terms of $\mathfrak{s}$ provide a superspace generalization of the Koszul-Tate resolution ($\delta$). In the linearized limit, the set of superspace differential operators that appear in $\mathfrak{s}$ 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.