Some Novel Features in 2D Non-Abelian Theory: BRST Approach

TL;DR

This paper explores novel features of 2D non-Abelian gauge theory within the BRST formalism, highlighting new symmetries, coupled Lagrangians, and the incorporation of CF-type restrictions using fermionic Lagrange multipliers.

Contribution

It introduces the existence of coupled (but equivalent) Lagrangian densities with (anti-)co-BRST symmetry and incorporates CF-type restrictions via fermionic Lagrange multipliers, a novel approach in BRST formalism.

Findings

Identification of coupled (but equivalent) Lagrangian densities with (anti-)co-BRST symmetry.

Incorporation of CF-type restrictions through fermionic Lagrange multipliers.

Modified Lagrangians respect specific symmetries and CF-type constraints.

Abstract

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we discuss some novel features of a two (1+1)-dimensional (2D) non-Abelian 1-form gauge theory (without any interaction with matter fields). Besides the usual off-shell nilpotent and absolutely anticommutating (anti-)BRST symmetry transformations, we discuss the off-shell nilpotent and absolutely anticommutating (anti-)co-BRST symmetry transformations. Particularly, we lay emphasis on the existence of the coupled (but equivalent) Lagrangian densities of the 2D non-Abelian theory in view of the presence of (anti-)co-BRST symmetry transformations where we pin-point some novel features associated with the Curci-Ferrari (CF) type restrictions. We demonstrate that these CF-type restrictions can be incorporated into the (anti-)co-BRST invariant Lagrangian densities through the fermionic Lagrange multipliers which carry specific ghost numbers. The modified versions of the Lagrangian densities (where we get rid of the new CF-type restrictions) respect some precise symmetries as well as a couple of symmetries with CF-type constraints. These observations are completely novel as far as the BRST formalism, with proper (anti-)co-BRST symmetries, is concerned.