Finiteness of the chiral anomaly graph in higher dimensions

The chiral anomaly graph in 2n dimensions is shown to be completely finite, independent of any constraints which would be imposed from vector-current conservation or Bose-symmetry. There is an n-fold ambiguity present in the graph which guarantees that all current divergences are equivalent in all (self-consistent) perturbative regulating procedures. The chiral anomaly is shown to reside in the alternating sum of current divergences. The ambiguity structure of the chiral anomaly graph in the Pauli-Villars scheme is explicitly computed as a specific example of this general result.     

Dispersive derivation of the trace anomaly

We present a simple derivation of the one-loop trace anomaly in spinor QED through dispersion relations, avoiding completely any ultraviolet regularization. The anomaly can be expressed as a convergent sum rule for the imaginary part of a relevant formfactor. In the massless limit, the imaginary part produces a delta-function singularity at zero external momentum squared. Such a treatment reveals an “infrared face” of the trace anomaly, in striking similarity with the well-known case of the axial anomaly.     

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.     

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.     

Anomaly-free supergravity theories remain anomaly-free after dimensional reduction

We show that the anomaly after compactification of a supergravity theory coupled to Yang-Mills matter is usually given by an integral of the original anomaly over the compact space, as long as there are no isometries for the compact space. This means that a supergravity theory, whose anomaly vanishes identically (i.e., without the addition of local counter terms to the action), will remain anomaly-free after compactification to any lower dimension, subject to some restrictions on self-dual antisymmetric tensors. We next consider the case where the original anomaly cancels by the Green-Schwarz mechanism. In this case, again subject to the restrictions on self-dual antisymmetric tensors, the anomaly will still cancel after compactification to any lower dimension D > 2, provided that: (1) There are no U(1) gauge groups after compactification. (2) There exists a three-form field strength H such that dH = (TrR₀² + kTrF₀²), or that the compact space is chosen such that (TrR₀² + kTrF₀²) = 0.     

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.     

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.     

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.     

Scattering of 64 eV to 3 keV neutrons from polyethylene and graphite and the coherence length problem

We measured the neutron scattering intensity ratios from polyethylene (CH2) relative to graphite (C) at several discrete final energies, of narrow widths (approximately 3 eV) between 64 eV and 3 keV. The final energies were selected using a 238U filter. This experiment was carried out to search for any anomaly in the n-p scattered intensities from CH2 caused by the neutron coherence length. The scattered intensity ratios were found to conform to conventional expectations and no anomaly was observed.     

Trace anomalies and λφ4 theory in curved space

It is shown for a conformally invariant λφ⁴ theory in a weakly curved background, how to extend previous results to obtain full information about the trace anomaly in perturbation theory, including the “topological” term in the gravitational part of the anomaly. There is a strong connection among renormalisability of the curved space theory, finiteness of the energy-momentum tensor, and the role of normal products. Combined with a renormalisation-group analysis this provides an efficient means of calculating some terms in the anomaly to high orders of perturbation theory. In particular, the first λ-dependent coefficient of the topological part of the anomaly appears at O(λ⁴) and can be deduced from simple flat-space results without the calculation of any further Feynman diagrams. Some techniques based on an absorptive-part argument are developed in order to compute other anomalous coefficients, and a direct 5-loop calculation confirms the indirect renormalisation-group derivation of a non-vanishing R² anomaly at O(λ⁵). All the essential information can be obtained from the massless theory. The underlying ideas are applicable to other theories, and similar results for massless QED are obtained in a subsequent paper.     

Various Full Green Functions in QED

We are interested in deriving various full Green functions through general Ward–Takahashi identities (WTIs) for quantized field theories. With the help of a postulate of gauge group parameter, the general local gauge transformation laws preserving the gauge-invariance of the generating functional itself of QED model have been established successfully. By using path-integral technique, the various WTIs with resulting anomaly terms are derived under the gauge transformations. The arising of Jacobian factor from the integration measure gives a viable possibility to express full Green function. As a consequence, the complete expressions of the full vector, the full axial-vector, the full tensor vertex functions and so on are presented respectively by solving the complete set of the WTIs in the momentum space without considering the constraint imposing any Ansatz. In addition, anomaly function also provides an effective means to judge the divergence of variant coupling currents on fields.     

Absence of anomaly in Witten-type compactification

In the case of Witten-type compactification, we provide a general proof of the conjecture that any anomaly-free theory will remain anomaly free in compactified dimensions.     

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.     

Hypercharge flux, exotics, and anomaly cancellation in F-theory grand unification

We sharpen constraints related to hypercharge flux in F-theory grand unified theories that possess U(1) symmetries and argue that they arise as a consequence of four-dimensional anomaly cancellation. This gives a physical explanation for all restrictions that were observed in spectral cover models while demonstrating that the phenomenological implications for a well-motivated set of models are not tied to any particular formalism.     

Study of the invar effect through ultrasonic measurements of the elastic properties of Fe(64)Ni(36) under pressure

The elastic properties of a polycrystalline sample of invar Fe(64)Ni(36) have been investigated at ambient temperature by ultrasonic experiments up to 7 GPa. The pressure dependence of the bulk modulus is extracted without using any model and discussed in terms of invar anomaly models.     

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.     

The aetiology of sigma model anomalies

Certain nonlinear sigma models with fermions are ill-defined due to an anomaly which exhibits characteristics of both the nonabelian gauge theory anomaly and the SU(2) anomaly. The simplest way to diagnose the anomaly involves consideration of the global topology of the theory. We review the mathematical methods needed for this analysis and apply them to several supersymmetric sigma models. Some of these are found to be anomalous.     

Algebraic renormalization of parity-preserving QED3 coupled to scalar matter I: unbroken case

In this letter the algebraic renormalization method, which is independent of any kind of regularization scheme, is presented for the parity-preserving QED₃ coupled to scalar matter in the symmetric regime, where the scalar assumes vanishing vacuum expectation value, = 0. The model shows to be stable under radiative corrections and anomaly free.     

Lattice vibrational properties of TmTe

We have investigated the lattice dynamical properties of a TmTe compound by using a breathing shell model suitable for this compound. The calculated phonon dispersion curves (PDC) reveal that this compound does not show any anomaly in their phonon properties. Our results on PDC, phonon density of states and lattice specific heat reveal that the phonon properties of this compound are like the other rare earth chalcogenides, particularly Eu-chalcogenides. We emphasize the need of measurements of the complete PDC of TmTe to support the present results on the calculated phonon properties.