A Geometric Approach to Massive p-form Duality

TL;DR

This paper presents a geometric framework for understanding dualities in massive abelian p-form theories, focusing on the Topologically Massive and Self-Dual models in 2+1 dimensions, using dual non-local operators.

Contribution

It introduces a geometric representation for massive p-form theories that simplifies the description of dual models with a single non-local operator.

Findings

Unified geometric representation for dual models

Identification of a single non-local operator for observables

Insights into the phase space structure of massive p-forms

Abstract

Massive theories of abelian p-forms are quantized in a generalized path-representation that leads to a description of the phase space in terms of a pair of dual non-local operators analogous to the Wilson Loop and the 't Hooft disorder operators. Special atention is devoted to the study of the duality between the Topologically Massive and the Self-Dual models in 2+1 dimensions. It is shown that these models share a geometric representation in which just one non local operator suffices to describe the observables.