Free Abelian 2-Form Gauge Theory: BRST Approach

TL;DR

This paper explores the symmetry properties and algebraic structure of a 4D free Abelian 2-form gauge theory using BRST formalism, highlighting the role of a Curci-Ferrari type condition in ensuring symmetry consistency.

Contribution

It provides a detailed analysis of BRST, anti-BRST, and related symmetries in a 4D Abelian 2-form gauge theory, deriving the Curci-Ferrari condition from constraint analysis.

Findings

Nilpotent BRST and anti-BRST symmetries are absolutely anticommuting due to the Curci-Ferrari condition.

Conserved charges obey specific algebraic structures.

Curci-Ferrari type restriction derived from physicality criteria.

Abstract

We discuss various symmetry properties of the Lagrangian density of a four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. The present free Abelian gauge theory is endowed with a Curci-Ferrari type condition which happens to be a key signature of the 4D non-Abelian 1-form gauge theory. In fact, it is due to the above condition that the nilpotent BRST and anti-BRST symmetries of the theory are found to be absolutely anticommuting in nature. For our present 2-form gauge theory, we discuss the BRST, anti-BRST, ghost and discrete symmetry properties of the Lagrangian densities and derive the corresponding conserved charges. The algebraic structure, obeyed by the above conserved charges, is deduced and the constraint analysis is performed with the help of the physicality criteria where the conserved and nilpotent (anti-)BRST charges play completely independent roles. These physicality conditions lead to the derivation of the above Curci-Ferrari type restriction, within the framework of BRST formalism, from the constraint analysis.