Induced quantum curvature and three-dimensional gauge theories

The effects of quantum holonomy in three-dimensional gauge theories with massless fermions is examined and different definitions of the fermion determinant are discussed. The source of a global gauge and parity anomaly is identified in Schrödinger picture quantization as an induced holonomy that arises from the fermionic sector of the theory. In certain fermion representations this holonomy leads to a global obstruction to imposing either gauge or parity invariance through the implementation of Gauss' law constraint. However, such obstructions can be removed by exploiting renormalization ambiguities inherent in the definition of composite operators.     

A supersymmetric gluon model

It is pointed out that parity doubling does not provide a satisfactory resolution of the conflict between parity and fermion-number conservation in supersymmetric gauge theories. A new generalized gauge principle is proposed which overcomes this difficulty for both Abelian and non-Abelian local symmetries.     

Anomalies and gauge symmetry

Anomalies are known to have an intrinsic geometrical meaning. Using a formalism where the gauge condition is never made explicit we reanalyze the gauge theory anomaly problem. By requiring simultaneously the BRS and anti-BRS invariances, we do not need to use in our study the gauge dependent anti-ghost equation of motion. Then all equations definining the anomaly are independent of all parameters specifying the lagrangian. Not only does this stress explicitly the geometrical nature of the anomaly problem, but it allows for a single analysis for all possible BRS and anti-BRS invariant gauges, including those with four-ghost interactions. Our method for solving the anomaly equations is as a new sign of the relevance of the formalism in which the ghost components are unified with those of the classical gauge field, the ghost fields playing the role of a “connection” along unphysical directions. We recover the ABJ anomaly directly from the structure of BRS equations, as a straightforward application of the Chern-Weil theorem in some enlarged space. The method can be formally extended to higher space-time dimensions, and a general formula for “anomalies” in any even dimension is given.     

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.     

The anomaly in the Slavnov identity for N = 1 supersymmetric Yang-Mills theories

We solve the consistency conditions of the BRS symmetry in a general N = 1 sypersymmetric Yang-Mills theory with semi-simple gauge group. As a result we find uniquely the supersymmetric extension of the chiral anomaly. Its coefficient is calculated in one loop and does not, in general, vanish. This corrects our earlier statement on the absence of this anomaly.     

Overlap in odd dimensions

In odd dimensions the lattice overlap formalism is simpler than in even dimensions. Masslessness of fermions can still be preserved without fine tuning and gauge invariance without gauge averaging can be maintained, although, sometimes, only at the expense of parity invariance. When parity invariance is enforced invariance under small gauge transformations can be maintained and continuum global gauge anomalies are reproduced.     

Classical versus quantum trace for supersymmetric gauge fields

I calculate the effective action for a supersymmetric Schwinger model in a two-dimensional supergravity background and prove that the gauge superfield does not contribute to the trace anomaly in spite of its classical Weyl non-invariance.     

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).     

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.     

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 new gauge theory without an elementary photon

A gauge theory is formulated in two spatial dimensions different from all gauge theories previously known. Unlike quantum electrodynamics in such a space there does not exist an elementary photon in the model, even though a bound state having appropriate quantum numbers can be induced for weak coupling to a spinor field. Particularly noteworthy is the fact that despite the demonstrated covariance of the theory, there is an anomaly (i.e., noncanonical) term in the spatial transformation of the charge bearing field.     

On the quantization of anomalous theories

The possible definition of the Gauss' law operator in an anomalous gauge theory is discussed. It is shown that the most natural choice does not lead to any anomaly in the commutation rules. The case of two-dimensional theories is considered.     

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.     

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.     

Elliptic index and superstring effective actions

Certain N = 1 supersymmetric string one-loop effective actions can be obtained directly from the path integral. As the computation is essentially the same as the one leading to the index of the Dirac-Ramond operator, they are determined by the gauge and gravitational anomaly structure of the theory. Specifically, we calculate the four-point effective action in ten dimensions, the corrections to the kinetic terms in d = 6 (including auxiliary fields) and the Fayet-Iliopoulos D-term in d = 4. We also compute the β-function of four-dimensional N = 2 theories from the elliptic genus in d = 6. Furthermore, we derive supersymmetry Ward type identities in terms of Kac-Moody characters, relating parity conserving with parity violating amplitudes.     

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.     

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.     

Parity violating Compton amplitude in unified theories

The leading contribution of O(αG_F) to the parity violating piece of the electron Compton amplitude is calculated in the Weinberg Salam unified theory and is shown to vanish. The reason for this is the nonexistence of parity violating charge and electric dipole moment. In the computation, a problem with the usual gauge fixing terms in the Weinberg model was encountered and resolved; the gauge fixing terms made it impossible to satisfy the electromagnetic Ward identity off mass-shell. The resolution of this problem has led to changed Feynman rules resulting in fewer graphs and gauge dependent vertices. Further features are a renormalization of the parity violating infinities, and a discussion of how the γ₅-algebra and n-dimensional regularization can coexist peacefully.     

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.     

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.