Global Anomalies in the Batalin Vilkovisky Quantization

TL;DR

This paper extends the Batalin Vilkovisky quantization method to include global anomalies, enabling the calculation of Ward identities involving global currents, demonstrated through the axial model and the Adler Bell Jackiw anomaly.

Contribution

It introduces a novel extension of BV quantization to handle global anomalies by trivially gauging global Abelian symmetries, allowing calculation of related Ward identities.

Findings

Extended BV method can compute global anomalies.

Successfully applied to axial model and ABJ anomaly.

No additional obstructions introduced in the master equation.

Abstract

The Batalin Vilkovisky (BV) quantization provides a general procedure for calculating anomalies associated to gauge symmetries. Recent results show that even higher loop order contributions can be calculated by introducing an appropriate regularization-renormalization scheme. However, in its standard form, the BV quantization is not sensible to quantum violations of the classical conservation of Noether currents, the so called global anomalies. We show here that the BV field antifield method can be extended in such a way that the Ward identities involving divergencies of global Abelian currents can be calculated from the generating functional, a result that would not be obtained by just associating constant ghosts to global symmetries. This extension, consisting of trivially gauging the global Abelian symmetries, poses no extra obstruction to the solution of the master equation, as it happens in the case of gauge anomalies. We illustrate the procedure with the axial model and also calculating the Adler Bell Jackiw anomaly.