Abelian and non-Abelian anomalies in monopole-fermion interactions

Abstract

Taking an example of the standard SU(5) theory, the monopole-fermion system is reduced to an effective 2-dimensional model. This is a generalized Schwinger model containing four Abelian gauge fields interacting with N generations of massless fermions through vector and axialvector couplings. We quantize such a system exactly in the canonical operator formalism. Then, analyzing the cluster property of operators carrying various chiral charges, the roles of the Abelian and non-Abelian anomalies are studied in monopole-induced baryon decay. We demonstrate that the Abelian anomaly and the charge-mixing boundary condition are the driving forces for monopole-induced baryon decay, though the conservation law suggests the importance of the non-Abelian anomaly.