# Lorentz Violating $p$-form Gauge Theories in Superspace

## TL;DR

This paper explores how very special relativity (VSR) modifies the BRST and anti-BRST symmetries in superspace formulations of $p$-form gauge theories, revealing covariant structures with different Grassmann coordinate requirements.

## Contribution

It introduces VSR-modified extended BRST and anti-BRST invariant superspace formulations for $p=1,2,3$-form gauge theories within the BV framework, highlighting their covariant expressions.

## Key findings

- VSR modified BV actions can be expressed covariantly in superspace.
- One Grassmann coordinate suffices for BRST invariance in VSR.
- Two Grassmann coordinates are needed for combined BRST and anti-BRST invariance.

## Abstract

Very special relativity (VSR) keeps the main features of special relativity but breaks rotational invariance due to an intrinsic preferred direction. We study the VSR modified extended BRST and anti-BRST symmetry of the Batalin-Vilkovisky (BV) actions corresponding to the $p=1,2,3$-form gauge theories. Within VSR framework, we discuss the extended BRST invariant and extended BRST and anti-BRST invariant superspace formulations for these BV actions. Here we observe that the VSR modified extended BRST invariant BV actions corresponding to the $p=1,2,3$-form gauge theories can be written manifestly covariant manner in a superspace with one Grassmann coordinate. Moreover, two Grassmann coordinates are required to describe the VSR modified extended BRST and extended anti-BRST invariant BV actions in a superspace. These results are consistent with the Lorentz invariant (special relativity) formulation.