Total instanton restriction via multiverse interference: Noncompact gauge theories and (-1)-form symmetries

TL;DR

This paper explores how to eliminate instantons in local quantum field theories by topologically gauging (-1)-form symmetries, leading to a continuous family of universes and clarifying the decomposition in 2D gauge theories.

Contribution

It introduces a method to restrict instantons via multiverse interference and applies it to 2D gauge theories, expanding understanding of decomposition and anomalies.

Findings

Elimination of instantons through topological gauging of (-1)-form symmetries.

Clarification of the Gross-Taylor string interpretation of decomposition.

Identification of analogues of the Witten effect in universe rotations.

Abstract

In this note we consider examples of decomposition (in which a local QFT is equivalent to a disjoint union of multiple independent theories, known as universes) where there is a continuous familiy of universes, rather than a finite or countably infinite collection. In particular, this allows us to consistently eliminate all instantons in a local QFT via a suitable topological gauging of the (-1)-form symmetry. In two-dimensional U(1) gauge theories, this is equivalent to changing the gauge group to R. This makes both locality as well as the instanton restriction explicit. We apply this to clarify the Gross-Taylor string interpretation of the decomposition of two-dimensional pure Yang-Mills. We also apply decomposition to study two-dimensional R gauge theories, such as the pure R Maxwell theory, and two-dimensional supersymmetric gauged linear sigma models whose gauge groups have factors of R. In that context, we find that analogues of the Witten effect for dyons, here rotating between universes, play a role in relating anomalies of the individual universes to (different) anomalies in the disjoint union. Finally, we discuss limits of the Tanizaki-Unsal construction, which accomplish instanton restriction by topologically gauging a Q/Z (-1)-form symmetry, and speculate in two-dimensional theories on possible interpretations of those limits in terms of the adelic solenoid.