# Nilpotent (Anti-)BRST and (Anti-)co-BRST Symmetries in 2D non-Abelian Gauge Theory: Some Novel Observations

## TL;DR

This paper explores novel features of nilpotent (anti-)BRST and (anti-)co-BRST symmetries in 2D non-Abelian gauge theory, revealing unique algebraic structures and cohomological relationships with implications for gauge symmetry analysis.

## Contribution

It introduces new algebraic and cohomological insights into 2D non-Abelian gauge theories, emphasizing the existence of a single Lagrangian respecting these symmetries and highlighting novel properties of (anti-)co-BRST symmetries.

## Key findings

- Existence of a single Lagrangian density with proper symmetry algebra
- Novel properties of (anti-)co-BRST symmetries in 2D gauge theory
- Distinct features of Curci-Ferrari type restrictions in this context

## Abstract

We discuss the nilpotent Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and (anti-)co-BRST symmetry transformations and derive their corresponding conserved charges in the case of a two (1+1)-dimensional (2D) self-interacting non-Abelian gauge theory (without any interaction with matter fields). We point out a set of novel features that emerge out in the BRST and co-BRST analysis of the above 2D gauge theory. The algebraic structures of the symmetry operators (and corresponding conserved charges) and their relationship with the cohomological operators of differential geometry are established, too. To be more precise, we demonstrate the existence of a single Lagrangian density that respects the continuous symmetries which obey proper algebraic structure of the cohomological operators of differential geometry. In literature, such observations have been made for the coupled (but equivalent) Lagrangian densities of the 4D non-Abelian gauge theory. We lay emphasis on the existence and properties of the Curci-Ferrari (CF) type restrictions in the context of (anti-)BRST and (anti-)co-BRST symmetry transformations and pinpoint their key differences and similarities. All the observations, connected with the (anti-)co-BRST symmetries, are completely novel.