Circle compactification and ’t Hooft anomaly

Abstract

Abstract Anomaly matching constrains low-energy physics of strongly-coupled field theories, but it is not useful at finite temperature due to contamination from high-energy states. The known exception is an ’t Hooft anomaly involving one-form symmetries as in pure SU(N ) Yang-Mills theory at θ = π. Recent development about large-N volume independence, however, gives us a circumstantial evidence that ’t Hooft anomalies can also remain under circle compactifications in some theories without one-form symmetries. We develop a systematic procedure for deriving an ’t Hooft anomaly of the circle-compactified theory starting from the anomaly of the original uncompactified theory without one-form symmetries, where the twisted boundary condition for the compactified direction plays a pivotal role. As an application, we consider ℤN $$ {\mathbb{Z}}_N $$ -twisted ℂPN−1 $$ \mathbb{C}{P}^{N-1} $$ sigma model and massless ℤN $$ {\mathbb{Z}}_N $$ -QCD, and compute their anomalies explicitly.

Keywords

• Anomalies in Field and String Theories
• Global Symmetries
• Nonperturbative Effects