Noncommutative Gauge Theories: Model for Hodge theory

TL;DR

This paper constructs and analyzes various BRST symmetries in noncommutative gauge theories, demonstrating their algebraic structure aligns with de Rham cohomology and establishing these theories as models for Hodge theory.

Contribution

It introduces nilpotent BRST symmetries in noncommutative gauge theories and links their algebra to de Rham cohomology, providing a novel field-theoretic realization of Hodge theory.

Findings

BRST, anti-BRST, dual-BRST, anti-dual-BRST symmetries constructed for NC gauge theories

Noether charges satisfy algebra similar to de Rham cohomological operators

Noncommutative gauge theories serve as models for Hodge theory

Abstract

The nilpotent BRST, anti-BRST, dual-BRST and anti-dual-BRST symmetry transformations are constructed in the context of noncommutative (NC) 1-form as well as 2-form gauge theories. The corresponding Noether's charges for these symmetries on the Moyal plane are shown to satisfy the same algebra as by the de Rham cohomological operators of differential geometry. The Hodge decomposition theorem on compact manifold is also studied. We show that noncommutative gauge theories are field theoretic models for Hodge theory.