Finite-mode regularization of the fermion functional integral (II)

Using the finite-mode regularization introduced in a previous paper, we define the functional integral for a theory of Weyl fermions. We check this definition by making sure the resulting triangle anomaly satisfies the Wess-Zumino consistency conditions. We compare our result with others found in the literature. We apply the finite-mode regularization to compute the axial anomaly in any space-time dimension and to find the explicit expression of anomalous currents in terms of the gauge fields. We illustrate the phenomenon of the infrared compensation of the chiral anomaly.     

Hamiltonian Anomalies from Extended Field Theories

We develop a proposal by Freed to see anomalous field theories as relative field theories, namely field theories taking value in a field theory in one dimension higher, the anomaly field theory. We show that when the anomaly field theory is extended down to codimension 2, familiar facts about Hamiltonian anomalies can be naturally recovered, such as the fact that the anomalous symmetry group admits only a projective representation on the Hilbert space, or that the latter is really an abelian bundle gerbe over the moduli space. We include in the discussion the case of non-invertible anomaly field theories, which is relevant to six-dimensional (2, 0) superconformal theories. In this case, we show that the Hamiltonian anomaly is characterized by a degree 2 non-abelian group cohomology class, associated to the non-abelian gerbe playing the role of the state space of the anomalous theory. We construct Dai-Freed theories, governing the anomalies of chiral fermionic theories, and Wess-Zumino theories, governing the anomalies of Wess-Zumino terms and self-dual field theories, as extended field theories down to codimension 2.     

Gauge invariant theories of the generalized chiral Schwinger model

The gauge invariant theories of the generalized chiral Schwinger model are constructed in terms of two schemes with and without Wess-Zumino terms, respectively. Following the former scheme, we calculate the Wess-Zumino term which cancels the gauge anomaly, and then constitute the gauge invariant theory by adding the Wess-Zumino term to the original Lagrangian of the model. According to the latter, we modify the original Hamiltonian by adding a term composed of constraints of the model. It is so designed that the theory described by the modified Hamiltonian and its corresponding first-order Lagrangian maintains gauge invariance. We show by the canonical Dirac method that each of the two gauge invariant theories has the same physical spectrum as that of the original gauge noninvariant formulation.     

Gauge invariant theories of the generalized chiral Schwinger model

The gauge invariant theories of the generalized chiral Schwinger model are constructed in terms of two schemes with and without Wess-Zumino terms, respectively. Following the former scheme, we calculate the Wess-Zumino term which cancels the gauge anomaly, and then constitute the gauge invariant theory by adding the Wess-Zumino term to the original Lagrangian of the model. According to the latter, we modify the original Hamiltonian by adding a term composed of constraints of the model. It is so designed that the theory described by the modified Hamiltonian and its corresponding first-order Lagrangian maintains gauge invariance. We show by the canonical Dirac method that each of the two gauge invariant theories has the same physical spectrum as that of the original gauge noninvariant formulation.     

Solutions of theU(N)σ models with the Wess-Zumino term

We study finite action classical solutions of the Euclidean two-dimensionalU(N) sigma models with the Wess-Zumino term. We show that these solutions are related to (and so can be derived from) the solutions of the Lax-pair problem for the correspondingU(N) sigma model (without the Wess-Zumino term). We discuss the value of the action for these solutions and prove that all these solutions are unstable.     

Solutions of theU(N)σ models with the Wess-Zumino term

We study finite action classical solutions of the Euclidean two-dimensionalU(N) sigma models with the Wess-Zumino term. We show that these solutions are related to (and so can be derived from) the solutions of the Lax-pair problem for the correspondingU(N) sigma model (without the Wess-Zumino term). We discuss the value of the action for these solutions and prove that all these solutions are unstable.     

Evaluating fermion determinants through the chiral anomaly

A class of fermion operators whose determinants can be calculated exactly has recently been noted. We observe that typically such operators can be chirally rotated into the free Dirac operator; hence, their determinants are given by the chiral anomaly. Four-dimensional fermion determinants of this type are computed; the appearance of the Wess-Zumino anomaly term is noted.     

Effective chiral meson lagrangian with Weinberg and KSFR relations from microscopic four-quark interactions

An effective chiral meson lagrangian is derived from a microscopic quark lagrangian. It contains a partial Higgs mechanism for ϱ-A₁ mass splitting reproducing Weinberg and KSFR relations, and includes quartic derivative “Skyrme” terms and the gauges Wess-Zumino term. The connection to previous approaches deriving the effective lagrangian exclusively from the chiral anomaly including “normal-parity” terms is established.     

Supersymmetry anomalies and some aspects of renormalization

We show how the $\text{L}$-matrix elements avoid the problem of supersymmetry breaking by the gauge fixing and ghost terms for renormalization in the Wess-Zumino gauge. Possible origins of supersymmetry anomalies are discussed. Gauge and gravitational anomalies induce a supersymmetry anomaly which has two distinct terms, one of which is gauge invariant. We give the expression for the noninvariant term for 2n-dimensional spacetime and for the invariant part in four dimensions. This anomaly, although cohomologically nontrivial, is still consistent with result that in superspace no supersymmetry anomaly is generated.     

Local supersymmetry anomaly in two dimensions

We study the local supersymmetry anomaly by constructing an N = 1 (counted by Majorana-Weyl spinors) chiral supergravity model in two dimensions. There is the local supersymmetry anomaly as well as the gravitational anomaly. We obtain the linearized forms of these anomalies by perturbation calculation. The full non-linear forms are obtained by finding a solution to the Wess-Zumino consistency condition. These anomalies can be derived from the supersymmetric extension of the Chern-Simons invariant in three dimensions.     

ON THE TWO-DIMENSIONAL MON-LINEAR σ MODEL WITH WESS-ZUMINO TERM

The classical solutions of the two-dimensional non-linear σ model with Wess-Zumino term are shown to be equivalent to that without the Wess-Zumino term under a suitable transformation.     

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.     

The superconformal anomaly in the 1 + 1 dimensional Wess-Zumino model

The superconformal trace anomaly is worked out to one-loop order in perturbation theory for the 1+1 dimensional Wess-Zumino model.     

On the Gauge and BRST Invariance of the Chiral QED with Faddeevian Anomaly

Chiral Schwinger model with the Faddeevian anomaly is considered. It is found that imposing a chiral constraint this model can be expressed in terms of chiral boson. The model when expressed in terms of chiral boson remains anomalous and the Gauss law of which gives anomalous Poisson brackets between itself. In spite of that a systematic BRST quantization is possible. The Wess-Zumino term corresponding to this theory appears automatically during the process of quantization. A gauge invariant reformulation of this model is also constructed. Unlike the former one gauge invariance is done here without any extension of phase space. This gauge invariant version maps onto the vector Schwinger model. The gauge invariant version of the chiral Schwinger model for a=2 has a massive field with identical mass however gauge invariant version obtained here does not map on to that.     

Consistency condition and Piguet-Sibold equations for the supersymmetric nonabelian chiral anomaly

The Wess-Zumino consistency condition is verified explicitly for the anomaly of a single chiral superfield coupling to a background scalar superfield, using the expression for the anomaly obtained by a direct perturbative calculation. The proof is next extended to a verification of the whole set of Piguet-Sibold equations.     

反常、Chern-Simons上链

本文提出一种联络空间上同调的概念,建立这种上同调群与Chern-Simons型示性类系列的同态关系,给出它们在反常、Wess-Zumino有效作用与Schwinger项等问题上的应用;从而概括了Faddeev,宋行长,Zumino等人最近关于这些问题的探讨。 关键词：     

Associativity in Wess-Zumino model and Kac-Moody algebra

Topological quantization of the coefficient of the Wess-Zumino model is investigated in Hamilton formalism. Quantization is shown to be required from the associativity of the operators. Center of the Kac-Moody algebra is also quantized from the requirement of the associativity. We show that there is a monopole in the configuration space of the Wess-Zumino model and show the relationship with the quantization of the monopole charge. We have found a Schwinger term in the commutator of left- and right-currents. This is an anomaly in a purely bosonic theory.     

Two-dimensional fermion determinants as Wess-Zumino actions

It is shown that, for Weyl operators of a rather general type, the effective action can be expressed as a combination of Wess-Zumino terms. The representation generalizes the result of Polyakov and Wiegmann to curved manifolds.     

The chiral anomaly and goldstone-wilczek current in even dimensions

The form of the non-abelian anomaly is described in arbitrary even dimension when the gauge group contains explicit U(1) factors. An effective action is constructed which when varied under the group reproduces the anomaly. It constitutes a generalization of the Wess-Zumino action.     

Hamiltonian formulation of anomaly free chiral bosons

Starting out with an anomaly free lagrangian formulation for chiral scalars, which includes a Wess-Zumino term (to cancel the anomaly), we formulate the corresponding hamiltonian problem. Then we use the (quantum) Siegel invariance to choose a particular solution, which turns out to coincide with the one obtained by Floreanini and Jackiw.