Symmetry theta angles and topological Witten effects

Abstract

We introduce a large class of $\hat{I}¸$ angles in quantum field theory that we call symmetry $\hat{I}¸$ angles. Unlike conventional $\hat{I}¸$ angles whose definition depends on a choice of a path integral, symmetry $\hat{I}¸$ angles are intrinsic parameters of a quantum field theory that depend only on its symmetries. A frequent consequence of symmetry $\hat{I}¸$ 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 $\hat{I}¸$. Physically, topological Witten effects induce generalized Aharonov-Bohm effects. We show that these new $\hat{I}¸$ angles and Witten effects can appear in many familiar field theories.

82 pages, 18 figures