Quantization Of Anomalous Gauge Theories Research Articles

Supersymmetric nonlinear sigma models as anomalous gauge theories

We revisit supersymmetric nonlinear sigma models on the target manifold $CP^{N-1}$ and $SO(N)/SO(N-2)\times U(1)$ in four dimensions. These models are formulated as gauged linear models, but it is indicated that the Wess-Zumino term should be added to the linear model since the hidden local symmetry is anomalous. Applying a procedure used for quantization of anomalous gauge theories to the nonlinear models, we determine the form of the Wess-Zumino term, by which a global symmetry in the linear model becomes smaller in the action than the conventional one. Moreover, we analyze the resulting linear model in the $1/N$ leading order. Consequently, we find that the model has a critical coupling constant similar to bosonic models. In the weak coupling regime, the $U(1)$ local symmetry is broken but supersymmetry is never broken. In contrast to the bosonic case, it is impossible to find stable vacua in the strong coupling regime as far as in the $1/N$ leading order. These results are straightforwardly generalized to the case of the hermitian symmetric space.

BRST quantization of anomalous gauge theories.

It is shown how BRST quantization can be applied to a guage 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 nonanomalous theory. The trivial sector plays the role of a topological sector if the system is quantized without shifting the anomalies.

Anomalies and Wess-Zumino terms in an extended, regularized field-antifield formalism

Quantization of anomalous gauge theories with a closed, irreducible gauge algebra within the extended field-antifield formalism is further pursued. Using a Pauli-Villars (PV) regularization of the generating functional at one-loop level, an alternative form for the anomaly is found which involves only the regulator. The analysis of this expression allows to conclude that recently found ghost-number-one cocycles with nontrivial antifield dependence cannot appear in PV regularization. Afterwards, the extended field-antifield formalism is further completed by incorporating quantum effects of the extra variables, i.e., by explicitly taking into account the regularization of the extra sector. In this context, invariant PV regulators are constructed from non-invariant ones, leading to an alternative interpretation of the Wess-Zumino action as the local counterterm relating invariant and non-invariant regularizations. Finally, application of the above ideas to the bosonic string reproduces the well-known Liouville action and the shift (26 − D) → (25 − D) at one loop.

THE WESS–ZUMINO TERM IN THE FIELD–ANTIFIELD FORMALISM

We carry out an analysis of the quantization of anomalous gauge theories inside the Batalin–Vilkovisky scheme. Working on the chiral QCD2, we show that by considering the group elements as dynamical variables one is able to construct a local solution, the Wess–Zumino term, for the master equation. Thus the gauge independence of the generating functional is restored. Also, the BRST charge is built up showing that in the extended space this operator recovers the nilpotency.

Anomalies and the Quantum Theory of Chiral Matter on a Line

We review aspects of anomalies in quantum field theory, mainly the canonical quantization of anomalous gauge theories in two spacetime dimensions. This includes the unitary, Lorentz invariant quantization of the chiral Schwinger model; and quantization of nonabelian chiral bosons, described by a generalization of the Siegel action, away from “critical dimension”. Bosonization of chiral theories in background gauge and gravitational fields is extensively discussed via path integral methods.

Quantization of anomalous gauge theories on a lattice

We discuss advantages and disadvantages of three equivalent lattice actions proposed before for anomalous chiral gauge theories. Applications to the chiral Scwinger model and the 4 dimensional chiral QED are presented.

A SIMPLE MANNER FOR THE QUANTIZATION OF ANOMALOUS GAUGE THEORIES

The chiral Schwinger model is a massive vector theory at the quantum level. We construct the gauge invariant action using Stueckelberg formalism from this. Then the resulting action is exactly the same as the modified action obtained by path-integral formalism. We propose a simple manner for the quantization of anomalous gauge theories.

ON THE QUANTIZATION OF A THEORY WITH GLOBAL GAUGE ANOMALIES

It is shown that the Faddeev-Shatashvili approach to the quantization of anomalous gauge theories can be extended to the case of global gauge anomalies.

On the path-integral quantization of anomalous gauge theories

The path-integral quantization of anomalous gauge theories is discussed. From the necessity of the “gauge volume” integration, the Wess-Zumino action appears naturally and, as a consequence, the effective action becomes gauge invariant. An application to the chiral Schwinger model gives a concrete example.

Degrees of freedom and the quantization of anomalous gauge theories

We show, for the two-dimensional case, that the anomalous gauge theory of chiral fermions yields degrees of freedom whose number depends on the regularization procedure. For a particular regularization, the gauge fields have dim[ rG]-rank[ rG] surviving degrees of freedom, while for others this number changes to 2 dim[ rG] . Our procedure and results are compared with Faddeev's recent suggestions on how to quantize anomalous gauge theories. We conclude with some remarks on the four-dimensional case.