The Anomaly Structure of Regularized Supergravity

TL;DR

This paper investigates the anomaly structure of supergravity theories using Pauli-Villars regularization, revealing how anomalies arise and can be partially canceled, with implications for string compactifications and effective field theories.

Contribution

It introduces a detailed analysis of supergravity anomalies and proposes mechanisms for their partial cancellation, extending understanding of anomaly cancellation in string-derived supergravity models.

Findings

Pauli-Villars fields cancel most divergences but not all linear divergences.

Anomalies form a supermultiplet with conformal anomalies under certain conditions.

Partial cancellation achieved via Green-Schwarz mechanism, but full cancellation requires additional counterterms.

Abstract

On-shell Pauli-Villars regularization of the one-loop divergences of supergravity theories is used to study the anomaly structure of supergravity and the cancellation of field theory anomalies under a $U(1)$ gauge transformation and under the T-duality group of modular transformations in effective supergravity theories with three K\"ahler moduli $T^i$ obtained from orbifold compactification of the weakly coupled heterotic string. This procedure requires constraints on the chiral matter representations of the gauge group that are consistent with known results from orbifold compactifications. Pauli-Villars regulator fields allow for the cancellation of all quadratic and logarithmic divergences, as well as most linear divergences. If all linear divergences were canceled, the theory would be anomaly free, with noninvariance of the action arising only from Pauli-Villars masses. However there are linear divergences associated with nonrenormalizable gravitino/gaugino interactions that cannot be canceled by PV fields. The resulting chiral anomaly forms a supermultiplet with the corresponding conformal anomaly, provided the ultraviolet cut-off has the appropriate field dependence, in which case total derivative terms, such as Gauss-Bonnet, do not drop out from the effective action. The anomalies can be partially canceled by the four-dimensional version of the Green-Schwarz mechanism, but additional counterterms, and/or a more elaborate set of Pauli-Villars fields and couplings, are needed to cancel the full anomaly, including D-term contributions to the conformal anomaly that are nonlinear in the parameters of the anomalous transformations.