Generalized ’t Hooft anomalies on non-spin manifolds
Mohamed M. Anber, Erich Poppitz
Abstract
A bstract 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 ℛ c of N -ality n c , formulated on non-spin manifolds. We show how to study these theories on 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. 𝕋 4 ). We also show how to consistently formulate various chiral gauge theories on non-spin manifolds.
Topics & Concepts
Anomaly (physics)PhysicsSpin (aerodynamics)Gauge theoryFermionTheoretical physicsChiral anomalySymmetry (geometry)Mixed anomalyGauge (firearms)Gauge anomalyMathematical physicsParticle physicsQuantum mechanicsSupersymmetric gauge theoryMathematicsGeometryHistoryArchaeologyThermodynamicsQuantum Chromodynamics and Particle InteractionsBlack Holes and Theoretical PhysicsParticle physics theoretical and experimental studies