Tensor gauge fields in arbitrary representations of GL(D,R) : duality & Poincare lemma

TL;DR

This paper develops a mathematical framework to analyze gauge structures and dualities of free gauge fields in arbitrary representations of GL(D,R), generalizing the Poincare lemma for systematic solutions.

Contribution

It introduces a generalized de Rham complex and proves a new Poincare lemma applicable to arbitrary irreducible representations of GL(D,R).

Findings

Unified approach to gauge structure and duality in arbitrary representations.

Generalized Poincare lemma for systematic solutions.

Framework applicable to a broad class of gauge theories.

Abstract

Using a mathematical framework which provides a generalization of the de Rham complex (well-designed for p-form gauge fields), we study the gauge structure and duality properties of theories for free gauge fields transforming in arbitrary irreducible representations of GL(D,R). We prove a generalization of the Poincare lemma which enables us to solve the above-mentioned problems in a systematic and unified way.