Global anomalies in the Batalin-Vilkovisky quantization

Abstract

The Batalin-Vilkovisky ͑BV͒ quantization provides a general procedure for calculating anomalies associated with 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 socalled 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 happens in the case of gauge anomalies. We illustrate the procedure with the axial model and also calculating the Adler-Bell-Jackiw anomaly. ͓S0556-2821͑97͒04524-4͔

On the Batalin, Fradkin, Fradkina, and Tyutin quantization of first order systems

“…Under this last point of view, BFFT and Lagrangian compensating fields play similar roles. In several examples of Lagrangian descriptions it is proved that compensating fields also do not belong to the cohomology at ghost number one and can be used as well to extract anomalous expectation values of physically relevant quantities [9].…”

Compensating fields, bosonization and soldering in QCD2

“…Recent examples are those of Refs. [5,6] where a general procedure for calculating anomalous divergences of global currents in the field antifield framework was developed. In these articles, the introduction of compensating fields leads to quantum corrections to the master equation and therefore to additional terms in the quantum action.…”

“…On the other hand, in the chiral QCD 2 case, where the gauge field is coupled to the chiral current, the bosonic matter field transforms as an element of the gauge group. Therefore, if one tries to look at the introduction of compensating fields as in [5,6] from the bosonized point of view, one faces the problem of how to find the appropriate bosonized version of the theory. Considering the case of a pure vector coupling, like QCD 2 , the corresponding bosonized version is well known.…”

“…This work is organized as follows: in section (2) we briefly review the ideas of references [5,6] and present the corresponding results for the case of QCD 2 . In section (3) the Abelian version of the model discussed in section (2) is bosonized using the soldering techniques.…”

“…A fundamental question arises when we introduce compensating fields: are the corresponding new symmetries obstructed by quantum effects? Several examples, within a Lagrangian formalism, show that compensating fields do not add new anomalies [4,5,6]( in other words, they do not change the BRST cohomology [7] ). It can be shown that this is also the case within Hamiltonian descriptions [8].…”