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Register a new userGeneralized t Hooft anomalies on non-spin manifolds
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We study the mixed anomaly between the discrete chiral symmetry and general baryon-color-flavor (BCF) backgrounds in $SU(N_c)$ gauge theories with $N_f$ flavors of Dirac fermions in representations ${cal R}_c$ of $N$-ality $n_c$, formulated on non-spin manifolds. We show how to study these theories on $mathbb{CP}^2$ by turning on general BCF fluxes consistent with the fermion transition functions. We consider several examples in detail and argue that matching the anomaly on non-spin manifolds places stronger constraints on the infrared physics, compared to the ones on spin manifolds (e.g.~$mathbb{T}^4$). We also show how to consistently formulate various chiral gauge theories on non-spin manifolds.
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We investigate a higher-group structure of massless axion electrodynamics in $(3+1)$ dimensions. By using the background gauging method, we show that the higher-form symmetries necessarily have a global semistrict 3-group (2-crossed module) structure, and exhibit t Hooft anomalies of the 3-group. In particular, we find a cubic mixed t Hooft anomaly between 0-form and 1-form symmetries, which is specific to the higher-group structure.
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