Abstract
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. \U0001d54b4). We also show how to consistently formulate various chiral gauge theories on non-spin manifolds.
Highlights
Anomalies is a currently active area of research with contributions coming from the highenergy, condensed matter, and mathematical communities
Summary: We continue our study [20] of the generalized ’t Hooft anomalies in SU(Nc) gauge theories with Nf flavors of Dirac fermions in representations Rc of Nc-ality nc. These theories have exact global discrete chiral symmetries. Considering these theories on T4 and turning on the most general ’t Hooft flux [21] backgrounds for the global symmetries, consistent with their faithful action, we found a mixed anomaly between the discrete chiral symmetry and the U(Nf )/ZNc baryon-color-flavor, or “BCF”, background
We showed that matching this BCF anomaly imposes new constraints on possible scenarios for IR physics, in addition to those imposed by the “traditional” 0-form ’t Hooft anomalies
Summary
We consider SU(Nc) gauge theories with Nf flavors of Dirac fermions transforming in a representation Rc of N-ality nc. The gauge group that faithfully acts on the fermions is SU(Nc) , where p. We consider SU(Nc) gauge theories with Nf flavors of Dirac fermions transforming in a representation Rc of N-ality nc.. The gauge group that faithfully acts on the fermions is SU(Nc) , where p. After modding out the redundant symmetries, we find that the 0-form global symmetry of the theory is Gglobal = SU(Nf )L × SU(Nf )R × U(1)B × Z2 dim(Rf )TRc , Z Nc × ZNf × Z2 p (2.1). We assume that Z2 dim(Rf )TRc is a genuine symmetry of the theory; it cannot be absorbed in the continuous part of Gglobal (this can be checked on a case by case basis). Notice that the ultraviolet fermions are taken to transform in the defining representation of the flavor group SU(Nf ), and we should use nf = 1. We keep the N -ality of the fermions under SU(Nf ) an arbitrary integer for the sake of generality
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