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

TL;DR

The paper develops a general framework in which a local QFT can decompose into a continuous family of universes via topological gauging of (-1)-form symmetries, enabling total instanton restriction in two dimensions by promoting U(1) to the noncompact group ${ m R}$. It provides detailed consistency checks by connecting this decomposition to changes in the gauge group (e.g., $U(1) ightleftarrows{ m R}$) and extends the analysis to sigma models, GLSMs, and SUSY settings, including Z-gerbes and their GLSM realizations. The work also analyzes the Tanizaki-Ünsal construction and explores limits, such as gauging ${ m Q}/{ m Z}$, with speculative interpretations in terms of adelic solenoids. Overall, the study offers a unifying picture where decomposition and multiverse interference yield controlled instanton restrictions and illuminate the role of noncompact gauge groups in low-dimensional quantum field theories.

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.