Hodge decomposition theorem for Abelian two form gauge theory

TL;DR

This paper demonstrates that a 2-form gauge theory in four dimensions exhibits a rich symmetry structure analogous to Hodge theory, with multiple nilpotent and bosonic symmetries related to de Rham cohomology operators.

Contribution

It establishes a Hodge decomposition framework within a 2-form gauge theory, revealing new dual symmetries and algebraic structures similar to differential geometry.

Findings

Identification of dual BRST symmetries in 2-form gauge theory

Correspondence between symmetry generators and de Rham cohomology operators

Derivation of extended BRST algebra with six conserved charges

Abstract

We show that the BRST/anti-BRST invariant 3+1 dimensional 2-form gauge theory has further nilpotent symmetries (dual BRST /anti-dual BRST) that leave the gauge fixing term invariant. The generator for the dual BRST symmetry is analogous to the co-exterior derivative of differential geometry. There exists a bosonic symmetry which keeps the ghost terms invariant and it turns out to be the analogue of the Laplacian operator. The Hodge duality operation is shown to correspond to a discrete symmetry in the theory. The generators of all these continuous symmetries are shown to obey the algebra of the de Rham cohomology operators of differential geometry. We derive the extended BRST algebra constituted by six conserved charges and discuss the Hodge decomposition theorem in the quantum Hilbert space of states.