Abstract
Continuing our exploration of maximally supersymmetric gauge theories (MSYM) deformed by higher dimensional operators, in this paper we consider an off-shell approach based on pure spinor superspace and focus on constructing supersymmetric deformations beyond the first order. In particular, we give a construction of the Batalin-Vilkovisky action of an all-order non-Abelian Born-Infeld deformation of MSYM in the non-minimal pure spinor formalism. We also discuss subtleties in the integration over the pure spinor superspace and the relevance of Berkovits-Nekrasov regularization.
Highlights
In this paper, we adopt the off-shell approach based on pure spinor superspace
It was not immediately obvious how to write down higher derivative deformations in this language. It was explained in [6] how the Born-Infeld deformation, to first order, can be constructed in the non-minimal pure spinor superspace formalism, and that the first order deformation in the Abelian case already gives a consistent action to all orders
We will develop this construction further, and show that the non-Abelian Born-Infeld deformation can be extended to all orders. (See [26,27,28,29,30,31,32,33,34,35] for previous works in the conventional component field formalism.) This is achieved in the BV formalism [36, 37], where the question of finding higher order deformations of the action that solve the BV master equation is turned into a problem of showing the triviality of certain cohomology classes
Summary
We review the construction of the action of maximally supersymmetric YangMills theories based on pure spinor superspace. A first attempt at constructing an action based on the Yang-Mills superfield involves a Chern-Simons type functional defined by an integration over the “minimal” pure spinor superspace. Rise to the correct SYM equation of motion up to pure gauge terms, provided that a truncation on the superfield is implemented. One extends the superfield to one defined over the non-minimal pure spinor superfields [6]. A conventional BRST invariant action may be obtained by imposing the Siegel gauge condition that effectively eliminates the BV anti-fields in the pure spinor superfield. The problem of finding supersymmetric higher derivative deformations turns into the problem of constructing higher derivative terms that solve the BV master equation [6]. We will see later that the closure of BV master equation order by order can be reformulated as a cohomology problem
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