Superfield Approach to Nilpotency and Absolute Anticommutativity of Conserved Charges: 2D non-Abelian 1-Form Gauge Theory

TL;DR

This paper uses an augmented superfield approach to analyze the nilpotency and anticommutativity of conserved charges in 2D non-Abelian gauge theory, revealing novel insights into (anti-)co-BRST symmetries without external restrictions.

Contribution

It introduces a novel application of AVSA to demonstrate properties of conserved charges in 2D non-Abelian gauge theory, especially highlighting differences between (anti-)BRST and (anti-)co-BRST symmetries.

Findings

Proves absolute anticommutativity without CF condition for (anti-)co-BRST charges.

Shows the nilpotency and invariance of charges within the superfield framework.

Identifies new results related to (anti-)co-BRST symmetries in 2D gauge theory.

Abstract

We exploit the theoretical strength of augmented version of superfield approach (AVSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism to express the nilpotency and absolute anticommutativity properties of the (anti-)BRST and (anti-)co-BRST conserved charges for the two $(1+1)$-dimensional (2D) non-Abelian 1-form gauge theory (without any interaction with matter fields) in the language of superspace variables, their derivatives and suitable superfields. In the proof of absolute anticommutativity property, we invoke the strength of Curci-Ferrari (CF) condition for the (anti-)BRST charges. No such outside condition/restriction is required in the proof of absolute anticommutativity of the (anti-)co-BRST conserved charges. The latter observation (as well as other observations) connected with (anti-)co-BRST symmetries and corresponding conserved charges are novel results of our present investigation. We also discuss the (anti-)BRST and (anti-)co-BRST symmetry invariance of the appropriate Lagrangian densities within the framework of AVSA. In addition, we dwell a bit on the derivation of the above fermionic (nilpotent) symmetries by applying the AVSA to BRST formaism where only the (anti-)chiral superfields are used.