Electric-Magnetic Duality of Topological Gauge Theories from Compactification

TL;DR

This paper explores the electric-magnetic duality in 4d topological gauge theories by analyzing their compactifications to 2 dimensions, revealing a strong-weak duality through exchange of degrees of freedom.

Contribution

It demonstrates how electric-magnetic duality manifests in compactified 2d TQFTs, connecting to phases in 4d gauge theories and discrete theta-angles.

Findings

Duality exchanges dynamical and background degrees of freedom.

Compactified TQFTs encode long-distance behavior of loop and surface operators.

Duality provides insights into phases not distinguishable by Wilson-'t Hooft criteria.

Abstract

In this note, we discuss electric-magnetic duality between a pair of 4d topological field theories (TQFTs) by considering their compactifications to 2 dimensions. These TQFTs control the long-distance behavior of loop and surface operators in 4d gauge theories with gapped phases. These were recently used in work by S. Gukov and A. Kapustin in detecting phases not distinguishable by the Wilson-'t Hooft criterion and by A. Kapustin and the author to construct discrete theta-angles for lattice Yang-Mills theories. The strong-weak duality is manifested in an exchange of dynamical and background degrees of freedom in the compactified TQFTs.