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

A bstract 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 family 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-Ünsal 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.