Instantons, Symmetries and Anomalies in Five Dimensions

TL;DR

This paper investigates a mixed 't Hooft anomaly between instantonic $U(1)_I$ symmetry and one-form center symmetry in five-dimensional gauge theories, revealing obstructions to coupling background fields and implications for phase structure.

Contribution

It identifies a finite-order mixed anomaly in 5D gauge theories involving instanton and center symmetries, and explores its consequences for supersymmetric theories and symmetry enhancement.

Findings

Obstruction to coupling $U(1)_I$ to background gauge fields in presence of one-form symmetry.

Existence of a mixed 't Hooft anomaly between instanton and center symmetries.

Implications for phase structure and symmetry enhancement in 5D supersymmetric gauge theories.

Abstract

All five-dimensional non-abelian gauge theories have a $U(1)_I$ global symmetry associated with instantonic particles. We describe an obstruction to coupling $U(1)_I$ to a classical background gauge field that occurs whenever the theory has a one-form center symmetry. This is a finite-order mixed 't Hooft anomaly between the two symmetries. We also show that a similar obstruction takes place in gauge theories with fundamental matter by studying twisted bundles for the ordinary flavor symmetry. We explore some general dynamical properties of the candidate phases implied by the anomaly. Finally, we apply our results to supersymmetric gauge theories in five dimensions and analyze the symmetry enhancement patterns occurring at their conjectured RG fixed points.