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 \( {\mathbb{Z}}_N \) -twisted \( \mathbb{C}{P}^{N-1} \) sigma model and massless \( {\mathbb{Z}}_N \) -QCD, and compute their anomalies explicitly.
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Tanizaki, Y., Misumi, T. & Sakai, N. Circle compactification and ’t Hooft anomaly. J. High Energ. Phys. 2017, 56 (2017). https://doi.org/10.1007/JHEP12(2017)056
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DOI: https://doi.org/10.1007/JHEP12(2017)056