Circle compactification and 't Hooft anomaly

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 $\theta =\pi$. 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 ${\mathbb{Z}}_N$-twisted $\mathbb{C}{P}^{N-1}$ sigma model and massless ${\mathbb{Z}}_N$-QCD, and compute their anomalies explicitly.

22 pages; (v2) references updated, minor changes

References in corpus (11)

• Generalized Global Symmetries
• Volume independence in large Nc QCD-like gauge theories
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Anomalies of discrete symmetries in three dimensions and group cohomology
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• Finite size phase transitions in QCD with adjoint fermions
• Vacuum structure of bifundamental gauge theories at finite topological angles
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Order parameters and color-flavor center symmetry in QCD
• The quarkynic phase and the Z_{Nc} symmetry

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