We study the mixed anomaly between the discrete chiral symmetry and general baryon-color-flavor (BCF) backgrounds in SU(Nc) gauge theories with Nf flavors of Dirac fermions in representations ℛc of N -ality nc, formulated on non-spin manifolds. We show how to study these theories on ℂℙ2 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. 𝕋4). We also show how to consistently formulate various chiral gauge theories on non-spin manifolds.
Anber, M. M., & Poppitz, E. (2020). Generalized ’t Hooft anomalies on non-spin manifolds. Journal of High Energy Physics, 2020(4), Article 97. https://doi.org/10.1007/jhep04%282020%29097