Hidden supersymmetry and spectral asymmetry: Fermion number fractionization and anomalies in even and odd dimensions

Abstract

We discuss how a “hidden supersymmetry” of the underlying field theories can be used to interpret and to calculate fermion number fractionization, axial anomalies, and anomalies in odd dimensions. All of the above effects can be related to a corresponding Witten index Δ(β) defined using the hidden supersymmetry—thus providing a unified treatement for them. The relevance of the β dependence of the Witten index in the different cases is also discussed. Further, for the three-dimensional case, an expression for the parity violating part of the effective action at finite temperatures is obtained.