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Superspace BRST/BV operators of superfield gauge theories

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 ($δ$). 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.