Materializing Superghosts

TL;DR

This paper develops an off-shell BV formalism for 10-dimensional N=1 super Yang-Mills theory by utilizing the materialized ghost phenomenon, revealing a geometric structure involving pure spinors.

Contribution

It introduces a novel off-shell BV construction for 10D SYM using materialized ghosts and auxiliary fields, connecting to pure spinor formalism.

Findings

Constructed off-shell BV action with auxiliary fields

Identified geometric structure of ghosts as coordinates on a spinor manifold

Derived on-shell BV action matching previous results

Abstract

We construct the off-shell BV realization of N=1, d=10 SYM with 7 auxillary fields. This becomes possible due to materialized ghost phenomenon. Namely, supersymmetry ghosts are coordinates on a manifold B of 10-dimensional spinors with pure spinors cut out. Auxillary fields are sections of a bundle over B, and supersymmetry transformations are nonlinear in ghosts. By integrating out axillary fields we obtain on-shell supersymmetric BV action with terms quadratic in antifields. Exactly this on-shell BV action was obtained in our previous paper after integration out of auxiliary fields in the framework of Pure Spinor Superfield Formalism.