Wess-Zumino Condition Research Articles

Unitary, Anomalous Master Ward Identity and its Connections to the Wess–Zumino Condition, BV Formalism and $$L_\infty $$-algebras

AbstractThe C*-algebraic construction of QFT by Buchholz and one of us relies on the causal structure of space-time and a classical Lagrangian. In one of our previous papers, we have introduced additional structure into this construction, namely an action of symmetries, which is related to fixing renormalization conditions. This action characterizes anomalies and satisfies a cocycle condition which is summarized in the unitary anomalous Master Ward identity. Here (using perturbation theory) we show how this cocycle condition is related to the Wess–Zumino consistency relation and the consistency relation for the anomaly in the BV formalism, where the latter follows from the generalized Jacobi identity for the associated $$L_\infty $$ L ∞ -algebra. In addition, we give a proof that perturbative agreement (i.e., independence of a perturbative QFT on the splitting of the Lagrangian into free and interacting parts) can be achieved by finite renormalizations.

Anomalies from correlation functions in defect conformal field theory

In previous work, we showed that an anomaly in the one point function of marginal operators is related by the Wess-Zumino condition to the Euler density anomaly on a two dimensional defect or boundary. Here we analyze in detail the two point functions of marginal operators with the stress tensor and with the displacement operator in three dimensions. We show how to get the boundary anomaly from these bulk two point functions and find perfect agreement with our anomaly effective action. For a higher dimensional conformal field theory with a four dimensional defect, we describe for the first time the anomaly effective action that relates the Euler density term to the one point function anomaly, generalizing our result for two dimensional defects.

Anomalies in the ERG Approach

The antifield formalism adapted in the exact renormalization group is found to be useful for describing a system with some symmetry, especially the gauge symmetry. In the formalism, the vanishing of the quantum master operator implies the presence of a symmetry. The QM operator satisfies a simple algebraic relation that will be shown to be related to the Wess-Zumino condition for anomalies. We also explain how an anomaly contributes to the QM operator.

CALCULATION OF ANOMALIES IN GAUGE THEORIES USING A GEOMETRIC APPROACH

Gauge theory and anomalies which arise under quantization of these theories are formulated using differential geometric methods. The Wess–Zumino conditions are developed and some other relevant geometric properties of anomalies are mentioned. An elementary derivation of the non-Abelian anomaly in 2n dimensions is presented using this formalism.

Higher-loop anomalies and their consistency conditions in non-local regularization

An algebraic program of computation and characterization of higher-loop BRST anomalies is presented. We propose a procedure for disentangling a genuine local higher-loop anomaly from the quantum dressings of lower-loop anomalies. For such higher-loop anomalies we derive a local consistency condition, which is the generalisation of the Wess-Zumino condition for the one-loop anomaly. The development is presented in the framework of the field-antifield formalism, making use of a non-local regularization method. The theoretical construction is exemplified by explicitly computing the two-loop anomaly of chiral W 3 gravity. We also give, for the first time, an explicit check of the local two-loop consistency condition that is associated with this anomaly.

TOPOLOGICAL MEANING OF GAUGE ANOMALY AND GAUSSIAN FACTORS

We consider 2n-dimensional non-Abelian gauge anomaly which is derived from (2n+2)-dimensional chiral anomaly using Gaussian factor regularization. Using this expression, we show explicitly the equivalence between the solution of Wess-Zumino condition obtained from (2n+2) dimensions and the anomaly given Fujikawa's method in arbitrary dimensions explicitly by constructing a local counterterm. It is shown that our method is also applicable to open string theories.

General Solutions of Wess-Zumino Consistency Conditions for Axial-Vector Current Divergence Anomaly

The general solutions of the Wess-Zumino Consistency conditions for axial-vector current divergence anomaly are derived. The terms different from the Bardeen's anomaly in the solutions can be eliminated by using suitable counter terms which do not violate the vector-current conservation. Thus, the Wess-Zumino conditions can be considered to be necessary and sufficient for determining the structure of the minimal consistency axial anomaly up to a multiplicative constant factor.

Discussions on the General Solutions to the Wess-Zumino Conditions in Higher Dimensions

The general solutions to the Wess-Zumino(wZ) conditions in higher even dimensions are given. For odd dimensional cases we find no nontrivial solutions.

Effective action for supersymmetric chiral anomaly

It is shown that consistency conditions of the type of the Wess-Zumino conditions are necessary and sufficient conditions for local integrability of the supersymmetric chiral anomaly. It follows from the requirement of global integrability that the coefficient of the anomalous action is discrete. Explicit expressions are obtained for consistent anomalies and the corresponding functionals, which depend on superfields of various types.

A Comment on the Kl4 Decay in the Gauged Nonlinear Sigma Model with the Wess-Zumino Condition

A Comment on the Kl4 Decay in the Gauged Nonlinear Sigma Model with the Wess-Zumino Condition

Non-Abelian consistent chiral anomalies in supersymmetric gauge theories

A path-integral formulation of non-abelian chiral anomalies in supersymmetric gauge theories is presented. We derive chiral anomalies of the axial form and of the left-right symmetric form, both obeying the Wess-Zumino condition, and investigate their minimal superfield form.

Chiral anomalies and zeta-function regularization.

The zeta-function method for regularizing determinants is used to calculate the chiral anomalies of several field-theory models. In SU(N) gauge theories without ${\ensuremath{\gamma}}_{5}$ couplings, the results of perturbation theory are obtained in an unambiguous manner for the full gauge theory as well as for the corresponding external-field problem. If axial-vector couplings are present, different anomalies occur for the two cases. The result for the full gauge theory is again uniquely determined; for its nongauge analog, however, ambiguities can arise. The connection between the basic path integral and the operator used to construct the heat kernel is investigated and the significance of its Hermiticity and gauge covariance are analyzed. The implications of the Wess-Zumino conditions are considered.

Chiral anomaly and the Wess-Zumino condition.

The connection between the Wess-Zumino condition and the chiral anomaly is discussed in the path-integral framework. When the non-Abelian anomaly exists, the Dirac operator detDLSL can be specified in various ways. The different specifications of detDLSL in the path integral lead to different forms of Ward-Takahashi identities and to different definitions of composite current operators involved. The Wess-Zumino condition imposes the generalized Bose symmetry among the gauge vertices, and thus it introduces a particular definition of current operators. For example, the axial-vector hypercharge current of an SU(3) theory, which is constructed to be consistent with the Wess-Zumino condition and global chiral symmetry, may be reduced to a U(1) current of the SU(2) subtheory; this particular construction of the U(1) current, however, does not satisfy the Atiyah-Singer index theorem expected for the SU(2) theory. We also discuss a semiperturbative regularization which automatically gives the non-Abelian anomaly for chiral fermions in the presence of electroweak fields.