A mass-deformed BLG theory in Gribov-Zwanziger framework

TL;DR

This paper extends the Gribov-Zwanziger framework to the mass-deformed BLG theory in $ abla=1$ superspace, incorporating Gribov copies, horizon restriction, and BRST symmetry restoration, with detailed Ward identity computations.

Contribution

It introduces a novel application of the Gribov-Zwanziger approach to the mass-deformed BLG theory, including horizon restriction and BRST symmetry restoration in superspace.

Findings

Implementation of the Gribov horizon in BLG theory

Restoration of BRST symmetry with external sources

Derivation of Ward identities for the theory

Abstract

In this paper, we extend the Gribov-Zwanziger framework accounting for the existence of Gribov copies to the mass deformed Bagger--Lambert--Gustavsson (BLG) theory in $\mathcal{N} =1 $ superspace. The restriction of the domain of integration in the Euclidean functional integral to the first Gribov horizon is implemented, by adding a non-local horizon term to the effective action. Furthermore, the soft breaking of the BRST symmetry due to horizon term is restored with the help of external sources. We compute the various Ward identities for this theory relying on the Lie 3-algebras.