arXiv subjects
Publications and source records attributed to Nelson R. F. Braga.
The role of one loop order corrections in the triplectic quantization is discussed in the case of W2 theory. This model illustrates the presence of anomalies and Wess Zumino terms in this quantization scheme where extended BRST invariance is represented in a completely anticanonical form.
We discuss how the variational principle can be used as a criterion for choosing, among scalar field actions implying the same equation of motion, the appropriate one for the AdS/CFT correspondence.
An interesting tool for investigating the quantum features of a field theory is the introduction of compensating fields. For instance, the anomalous divergence of the chiral current can be calculated in the field-antifield formalism from an extended form of QCD with compensating fields. The interpretation of this procedure from the bosonized point of view, in the two dimensional case, crucially depends on the possibility of defining a bosonized version for the extended theory. We show, by using some recent results on the soldering of bosonized actions corresponding to chiral fermions, how is the mapping between bosonic and fermionic representations of this extended $QCD_2$. In the bosonic formulation the anomalous divergence of the chiral current shows up from the equations of motion of the compensating fields.
We compute the anomalous divergence of currents associated with global transformations in the antifield formalism, by introducing compensating fields that gauge these transformations. We consider the explicit case of the global axial current in QCD but the method applies to any global transformation of the fields.
We show that the generators of canonical transformations in the triplectic manifold must satisfy constraints that have no parallel in the usual field antifield quantization. A general form for these transformations is presented. Then we consider gauge fixing by means of canonical transformations in this Sp(2) covariant scheme, finding a relation between generators and gauge fixing functions. The existence of a wide class of solutions to this relation nicely reflects the large freedom of the gauge fixing process in the triplectic quantization. Some solutions for the generators are discussed. Our results are then illustrated by the example of Yang Mills theory.
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.
A BPHZ renormalized form for the master equation of the field antifiled (or BV) quantization has recently been proposed by De Jonghe, Paris and Troost. This framework was shown to be very powerful in calculating gauge anomalies. We show here that this equation can also be applied in order to calculate a global anomaly (anomalous divergence of a classically conserved Noether current), considering the case of QED. This way, the fundamental result about the anomalous contribution to the Axial Ward identity in standard QED (where there is no gauge anomaly) is reproduced in this BPHZ regularized BV framework.
It has recently been shown that the Field Antifield quantization of anomalous irreducible gauge theories with closed algebra can be represented in a BRST superspace where the quantum action at one loop order, including the Wess Zumino term, and the anomalies show up as components of the same superfield. We show here how the Chiral Schwinger model can be represented in this formulation.
We study the non-abelian extension for the splitting of a scalar field into chiral components. Using this procedure we find a non ambiguous way of coupling a non abelian chiral scalar field to gravity. We start with a (non-chiral) WZW model covariantly coupled to a background metric and, after the splitting, arrive at two chiral Wess-Zumino-Witten (WZW) models coupled to gravity.
It is shown that the quantum master equation of the Field Antifield quantization method at one loop order can be translated into the requirement of a superfield structure for the action. The Pauli Villars regularization is implemented in this BRST superspace and the case of anomalous gauge theories is investigated. The quantum action, including Wess Zumino terms, shows up as one of the components of a superfield that includes the BRST anomalies in the other component. The example of W2 quantum gravity is also discussed.
A superspace formulation for the Batalin Vilkovisky formalism (also called field-antifield quantization ) with extended BRST invariance (BRST and anti-BRST invariance ) for gauge theories with closed algebra is presented. In contrast to a recent formulation, where only BRST invariance holds off shell, two collective sets of fields are introduced and an off shell realization of the extended algebra in a superspace with two Grassmann coordinates is obtained. The example of the Yang Mills theory is also considered.
It is shown how the BRST quantization can be applied to a gauge invariant sector of theories with anomalously broken symmetries. This result is used to show that shifting the anomalies to a classically trivial sector of fields (Wess-Zumino mechanism) makes it possible to quantize the physical sector using a standard BRST procedure, as for a non anomalous theory. The trivial sector plays the role of a topological sector if the system is quantized without shifting the anomalies.
We show that the BV (Batalin Vilkovisky) action, formulated with an extended BRST symmetry (including the shift symmetry), is also invariant under an extended anti-BRST transformation (where the antifields are the parameters of the transformation), when the gauge fixing Lagrangian is both BRST and anti-BRST invariant. We show that for a general gauge fixing Lagrangian, the BV action can be written in a manifestly extended BRST invariant manner in a superspace with one Grassmann coordinate whereas it can be expressed in a manifestly extended BRST and anti-BRST invariant manner in a superspace with two Grassmann coordinates when the gauge fixing Lagrangian is invariant under both BRST and anti-BRST transformations.