Symmetry theta angles and topological Witten effects

TL;DR

This paper introduces symmetry theta angles as intrinsic parameters in quantum field theories, leading to generalized Witten effects that influence charge attachment and induce novel Aharonov-Bohm phenomena.

Contribution

It defines symmetry theta angles, explores their role in topological Witten effects, and demonstrates their presence in various familiar quantum field theories.

Findings

Symmetry theta angles are intrinsic parameters depending only on symmetries.

Topological Witten effects alter charge attachment to topological operators.

These effects induce generalized Aharonov-Bohm phenomena.

Abstract

We introduce a large class of $\theta$ angles in quantum field theory that we call symmetry $\theta$ angles. Unlike conventional $\theta$ angles whose definition depends on a choice of a path integral, symmetry $\theta$ angles are intrinsic parameters of a quantum field theory that depend only on its symmetries. A frequent consequence of symmetry $\theta$ angles is a phenomenon we call the topological Witten effect, which is a generalization of the standard Witten effect. Topological Witten effects modify which charged operators are attached to topological operators as a function of $\theta$. Physically, topological Witten effects induce generalized Aharonov-Bohm effects. We show that these new $\theta$ angles and Witten effects can appear in many familiar field theories.