Gauge anomaly cancellation in chiral gauge theories

We consider chiral fermions interacting minimally with abelian and non-abelian gauge fields. Using a path integral approach and exploring the consequences of a mechanism of symmetry restoration, we show that the gauge anomaly has null expectation value in the vacuum for both cases (abelian and non-abelian). We argue that the same mechanism has no possibility to cancel the chiral anomaly, what eliminates competition between chiral and gauge symmetry at full quantum level. We also show that the insertion of the gauge anomaly in arbitrary gauge invariant correlators gives a null result, which points towards anomaly cancellation in the subspace of physical state vectors.     

One-loop gauge anomaly in type-1 superstring theory

The vanishing of the hexagon gauge anomaly of type-I superstring was shown previously by Green and Schwarz in the case that the gauge group is SO(32). The result, as well as the finiteness f the one-loop amplitude, makes the superstring theory a candidate for the unified theory including gravity. The vanishing of the gauge anomaly can be established for all N-point functions. The one-loop gauge anomaly is shown to be absent if the gauge group is SO(32).     

On the harmonic gauge in the quantization of strings

We discuss the path integral quantization of the bosonic string in the (non-background covariant) harmonic gauge, confronting it with the recently proposed background covariant version. The critical dimension as well as the ghost number current anomaly is computed. Whereas the latter has been found to vanish in the background covariant harmonic gauge, we obtain the same result as in the conformal gauge. This apparent discrepancy is resolved by detecting a new anomaly pertaining to the background covariant version of the harmonic gauge.     

Supersymmetry anomally in two dimensions

In two dimensions we obtain a supersymmetric extension of a gauge anomaly, and find that this is the origin of a supersymmetry anomaly in the Wess-Zumino gauge. We also obtain an effective action whose variations give rise to the gauge and supersymmetry anomalies.     

Three-Generat ion Models from Global Gauge Anomaly-Free Theories

In this work, we show how a global gauge anomaly of a gauge group H can be computed from a local one of a larger gauge group G ⊃ H. We also show that the number f of generations is tied to the consistency of a gauge theory H with initially a Z_f gIobal gauge anomaly. We give some examples of SU(N) models, in different dimensions of spacetime, with three families.     

Calculation of the color axial anomaly on the basis of the gauge-invariant spatial point-splitting regularization

The nonsinglet axial anomaly is calculated by employing Schwinger’s point-splitting regularization of the interaction between fermions and a non-Abelian gauge field. This method makes it possible to obtain a covariant expression for the anomaly directly from the effective action for the gauge field. Previously, the anomaly under study was calculated by many other methods. However, all calculations based on the point-splitting regularization (from the pioneering study of Bardeen in 1969) involve a number of intermediate steps and subtractions of specially chosen polynomials in the field.     

Parity anomalies in gauge theories in 2 + 1 dimensions

It is shown that the introduction of massless fermions in an abelian gauge theory in 2 + 1 dimensions does not lead to any parity anomaly despite a non-commutativity of limits in the structure function of the odd part of the vacuum polarisation tensor. However, a parity anomaly does exist in non-abelian theories due to a conflict between gauge invariance under large gauge transformations and the parity symmetry.     

Is the axial anomaly really determined in a continuous non-perturbative regularization?

In the framework of a gauge invariant continuous and non-perturbative regularization scheme based on the smearing of point-like interactions by means of cutoff functions, we show that the axial anomaly, though cutoff independent, depends on the shape of the cutoff functions. The standard value for the strength of the axial anomaly is recovered if we assume that the regularized gauge invariant axial current is in addition local. Received: 11 July 2001 / Published online: 25 January 2002     

Axial anomaly in lattice abelian gauge theory in arbitrary dimensions

The axial anomaly of lattice abelian gauge theory on a hyper-cubic regular lattice in arbitrary even dimensions is investigated by applying the method of exterior differential calculus. The topological invariance, gauge invariance and locality of the axial anomaly determine the explicit form of the topological part. The anomaly is obtained up to a multiplicative constant for finite lattice spacing and can be interpreted as the Chern character of the abelian lattice gauge theory.     

A Particle-Picture Approach to Anomalies in Chiral Gauge Theories

The system of a chiral fermion field coupled to a background gauge field is considered. By taking what we call the particle picture and carefully defining the S-matrix in the Heisenberg picture, we investigate anomalous phenomena in this system. It is shown by explicit calculations that the gauge-field configuration with nonvanishing topological-charge causes anomalous production of particles that is directly responsible for the chiral U(1) anomaly. Unlike the chiral U(1) anomaly, the gauge anomaly, that is, gauge non-invariance of the S-matrix is a problem that arises in the phase of the S-matrix. It is shown that this phase is related to the freedom existing in the quantization method, and that a suitably chosen phase which of course is consistent with the equation of motion can remove the gauge anomaly. Finally, a modified form of path-integral quantization for this system is proposed.     

Remark on the consistent gauge anomaly in supersymmetric theories

We present a direct field theoretical calculation of the consistent gauge anomaly in the superfield formalism, on the basis of a definition of the effective action through the covariant gauge current. The scheme is conceptually and technically simple and the gauge covariance in intermediate steps reduces calculational labors considerably. The resultant superfield anomaly, being proportional to the anomaly d^abc=trT^a{T^b,T^c}, is minimal without supplementing any counterterms. Our anomaly coincides with the anomaly obtained by Marinković as the solution of the Wess–Zumino consistency condition.     

Gravitational anomalies: Antisymmetric tensor gauge field versus bispinor field

It is shown perturbatively that the gravitational anomaly of the chiral bispinor field is twice as large as that of the self-dual antisymmetric tensor gauge field; in the previous literature they were supposed to agree with each other. This implies that a naive application of Fujikawa's path integral method leads to a wrong result for the anomaly of the self-dual antisymmetric tensor gauge field.     

Axial-vector anomaly for Dirac-Kähler fermions on the lattice

The axial-vector current of Dirac-Kähler fermions on the lattice is studied. We consider a U(1) gauge theory in two dimensions as well as an SU(N) gauge theory in four dimensions. Using a short-distance expansion of the fermion propagator in an external gauge field, we show that the correct anomaly is reproduced in the continuum limit.     

On the absence of supersymmetry anomalies in gauge theories

It is shown that N = 2 non-abelian gauge theory can be renormalized consistent with gauge invariance, supersymmetry and unitarity. There is no perturbative supersymmetry anomaly: the proof is independent of any specific regulator.     

Lorentz anomaly in arbitrary dimensions

It is shown that the Lorentz invariance is broken in gauge theories of chiral Weyl fermions in flat space-time via one-loop quantum corrections. Abelian gauge fields contribute to this anomaly in even dimensions larger than or equal to four and non-Abelian gauge fields do in even dimensions larger than or equal to six. The anomaly is proportional toD/2–1 power to the charge, whereD is a number of space-time dimensions.     

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.     

Discrete gauge symmetry anomalies

It has been recently argued that quantum gravity effects strongly violate all non-gauge symmetries. This would suggest that all low energy discrete symmetries should be gauge symmetries, either continuous or discrete. Acceptable continuous gauge symmetries are constrained by the condition they should be anomaly free. We show here that any discrete gauge symmetry should also obey certain “discrete anomaly cancellation” conditions. These conditions strongly constrains the massles fermion content of the theory and follow from the “parent” cancellation of the usual continuous gauge anomalies. They have interesting applications in model building. As an example we consider the constraints on the Z_N “generalized matter parities” of the supersymmetric standard model. We show that only a few (including the standard R-parity) are “discrete anomaly free” unless the fermion content of the minimal supersymmetric standard model is enlarged.     

Cancellation of quadratically divergent mass corrections in globally supersymmetric spontaneously broken gauge theories

The one-loop quadratically divergent mass corrections in globally supersymmetric gauge theories with spontaneously broken abelian and non-abelian gauge symmetry are studied. Quadratically divergent mass corrections are found to persist in an abelian model with an ABJ anomaly. However, additional supermultiplets necessary to cancel the ABJ anomaly, turn out to be sufficient to eliminate the quadratic divergences as well, rendering the theory natural. Quadratic divergences are shown to vanish also in the case of an anomaly free model with spontaneously broken non-abelian gauge symmetry.     

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.