Topological Quantum Field Theory, Nonlocal Operators, and Gapped Phases of Gauge Theories

TL;DR

This paper explores the role of nonlocal operators in classifying gapped phases of 4D gauge theories, revealing new distinctions beyond traditional criteria and constructing associated topological quantum field theories.

Contribution

It introduces a novel framework using TQFTs and nonabelian gerbes to characterize phases with various condensates, extending understanding of gauge theory phase structure.

Findings

Surface operators can be confined, providing new phase distinctions.

Constructed TQFTs describe long-distance behavior of non-confined operators.

In dyonic phases, the theta-angle is quantized.

Abstract

We revisit the role of loop and surface operators as order parameters for gapped phases of four-dimensional gauge theories. We show that in some cases surface operators are confined, and that this fact can be used to distinguish phases which are not distinguished by the Wilson-'t Hooft criterion. The long-distance behavior of loop and surface operators which are neither confined nor screened is controlled by a 4d TQFT. We construct these TQFTs for phases which are characterized by the presence of electrically and/or magnetically charged condensates. Interestingly, the TQFT describing a phase with a nonabelian monopole condensate is based on the theory of nonabelian gerbes. We also show that in phases with a dyonic condensate the low-energy theta-angle is quantized.