Reducible gauge theories in very special relativity

Abstract

In this paper we analyze the tensor field (reducible gauge) theories in the context of very special relativity (VSR). Particularly, we study the VSR gauge symmetry as well as VSR BRST symmetry of Kalb-Ramond and Abelian 3-form fields involving a fixed null vector. We observe that the Kalb-Ramond and Abelian 3-form fields and corresponding ghosts get masses in the VSR framework. The effective action in VSR-type axial gauge is greatly simplified compared with the VSR-type Lorenz gauge. Further, we quantize these models using a Batalin-Vilkovisy (BV) formulation in VSR.

Lorentz violating p-form gauge theories in superspace

“…Also, it has been shown that the gauge field in the quantum gauge perspective naturally acquires mass without the conventional Higgs mechanism [7]. The modifications due to VSR have also been analyzed for the reducible gauge theories using the BV formulation [8]. Within the VSR framework, the event space underlying the dark matter and the dark gauge fields supports the algebraic structure [9].…”

“…Here we note that, in comparison to VSR-modified covariant gauges, the gauge-fixed Lagrangian density takes simplest form [8] in VSR-modified light-cone gauge, η · A = 0, where η μ is an arbitrary constant vector that defines a preferred axis in space. Now, the effective quantum Lagrangian density for Yang-Mills theory in VSR is given by…”

“…We further demonstrate a superspace description for the 2-form gauge theory having extended BRST invariance and extended anti-BRST invariance. To do so, we start with the classical Lagrangian density for Abelian rank-2 antisymmetric tensor field (B μν ) theory in VSR as [7,8] …”

“…VSR generalization to the tensor field (reducible gauge) theories has also been done using a BV formulation [7,8]. A rigorous construction of quantum field theory in VSR framwork is also studied [49].…”

“…In particular, we generalize our previous results for the case of Abelian 3-form gauge theory which is relevant as it plays a crucial role to study the excitations of the quantized versions of strings, superstrings and related extended objects. The classical Lagrangian density for the Abelian 3-form gauge theory in VSR is given by [7,8],…”