Preregularization And The Ambiguity Structure of the Jacobian for Chiral Symmetry Transformations

Abstract

Preregularization is a procedure for evaluating non-dimensionally- continued field theoretical amplitudes by constraining ambiguous terms within such amplitudes to absorb any Ward-identity violating terms that may arise. Usually these ambiguous terms correspond to some parametriz- able arbitrariness in the loop momenta percolating into shift-of- integration-variable surface terms peculiar to integer-dimensional space- time.^1,2,3 Indeed, since the proposal of preregularization, originally motivated to retain a spacetime structure consistent with supersymmetry,⁴ the procedure has been shown to be a “regularization-free” method for analyzing anomalies perturbatively. Preregularization enables a distinction to be made between the manifest finiteness of anomaly-generating amplitudes⁵ and the Ward-identity ambiguities associated with such amplitudes. In particular, preregularization has been shown to be applicable to the WA triangle anomaly,^2,4,6,7 two dimensional anomalies,^8,9 six-and- higher-dimensional anomalies,^9,10 a perturbative demonstration of the Adler Bardeen Theorem,¹¹ the supercurrent anomaly,¹² and (as discussed by Mann elsewhere in this volume) superstring anomalies. ¹³