Abelian duality in topological field theory

TL;DR

This paper establishes a topological abelian duality for finite gauge groups, extending the concept to finite homotopy TFTs and $ ext{pi}$-finite spectra using Brown-Comenetz duality, broadening the understanding of dualities in topological field theories.

Contribution

It introduces a topological abelian duality for finite gauge groups and extends it to finite homotopy TFTs of $ ext{pi}$-finite spectra using Brown-Comenetz duality.

Findings

Proves a topological abelian duality for finite gauge groups.

Extends duality to finite homotopy TFTs of $ ext{pi}$-finite spectra.

Uses Brown-Comenetz duality to generalize the duality framework.

Abstract

We prove a topological version of abelian duality where the gauge groups are finite abelian. The theories are finite homotopy TFTs, topological analogues of the $p$-form $U(1)$ gauge theories. Using Brown-Comenetz duality, we extend the duality to finite homotopy TFTs of $\pi$-finite spectra.