non-Abelian Anomaly Research Articles

Supersymmetric chiral effective action and nonabelian anomalies

The definition of the one-loop supersymmetric effective action for chiral superfields coupled to a nonabelian gauge superfield is carefully discussed. The variation of the odd parity part is not always integrable after regularisation, if anomalies are present. When this is compensated by a local additional term, so as to obtain an integral variation, a supersymmetric expression for the nonabelian anomaly, satisfying the Wess-Zumino consistency conditions, is simply obtained. The nonabelian anomaly is shown to be reproduced by relating it to the index for a Dirac-like operator defined on a two-dimensional disc in the space of gauge superfields. The integrated odd parity part of the effective action is further identified formally with the spectral asymmetry of a related Dirac-like operator involving one additional boson coordinate. The results are also expressed in terms of superforms which allow a connection to be made to general topological discussions of the anomaly. This depends on an analysis of the cohomology of superforms over flat superspace.

Abelian Anomaly, Non-Abelian Anomalies and Monopole-Induced Baryon Decay

Non-perturbative roles of the Abelian and non-Abelian anomalies are studied in baryon decay processes induced by monopoles as well as instantons.

CHERN-SIMONS COCHAIN AND ANOMALY

In this paper, we define a coboundary operator acting on the cochain in gauge potential space and establish a formula about Chern-Simons coboundary. The result can be employed to obtain the non-abelian anomaly, the gauge invariant Wess-Zumino effec-tive action and the Schwinger term etc. We show that the present approach covers Fad-deev's, Song's, and Zumino's approaches.

Consequences of the non-abelian anomaly in supersymmetric theories

In supersymmetric theories, the anomalous interactions involving the Goldstone supermultiplets are found not to be determined from symmetry considerations alone: they depend also on the dynamical details of the model. The origin of the unexpected results lies in the presence of the massless fermionic superpartners of the Goldstone bosons. For example, the decay π 0 → γγ is found to be suppressed in supersymmetric QCD (SQCD). Low-energy effective actions with the correct symmetry properties are constructed, taking SQCD as an illustrative example. The axion decay a → γγ in a supersymmetric composite model might be suppressed with the same mechanism that works for π 0 → γγ in SQCD.

Functional-integral approach to chiral anomalies in supersymmetric gauge theories

We formulate anomalous chiral and related Ward-Takahashi identities in supersymmetric-gauge theories, by generalizing Fujikawa’s functional-integral method to superspace. Our approach provides a manifestly supersymmetric and gauge-covariant treatment of the superspace Abelian anomalies, and is applicable to chiral- as well as to left-right symmetric theories. Non-Abelian anomalies are also discussed briefly. Superspace Abelian anomalies imply that particular composite operators,i.e. those containing the associatedU1 currents as a component, exhibit an anomalous supermultiplet structure. We discuss how this leads to various exact relations between scalar and gauge fermion condensates, thereby imposing strong constraints on possible chiral-symmetry realizations in supersymmetric-confining theories.

BRS cohomology and topological anomalies

The occurrence of non-abelian anomalies in gauge theories and gravitation, first discovered via perturbative techniques, is now completely explained from the mathematical point of view by means of the family index theorem of Atiyah and Singer. Here we make contact between this approach and BRS cohomology, by showing that they yield the same non-abelian anomalies, provided a certain restriction to “local” functionals is not introduced from the very beginning. In particular, this solves the “unicity” problem for this kind of anomalies. Local BRS cohomology is still relevant for the abelian case.

Anomalies and odd dimensions

The parity-violating effective action for theories of fermions coupled to external gauge and gravitational fields in odd dimensions is computed exactly. This action is then used to compute gauge and gravitational anomalies in even dimensions. This derivation of the anomalies elucidates the relation of covariant to consistent anomalies as well as the relation between the Abelian anomaly and the non-Abelian anomaly in two lower dimensions.

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.

The role of non-abelian anomalies and gauge invariance for the effective lagrangian of vector mesons

We note that gauge invariance, the Wess-Zumino term and the functional Legendre transform fixes almost uniquely the effective lagrangian for the π, ϱ, ω, A 1 system. It is shown that the only free parameters in L eff are ⨍ π , m ϱ 2, g ϱππ (and eventually α = ( fg/ m ϱ ) 2). Some phenomenological implications of the flavor anomalies are discussed; in particular a recent analysis on the status of the KSFR sum rule, the m A 1 2 = 2 m ϱ 2 relation and the ω → 3 π contact term are critically revisited.

Hamiltonian interpretation of anomalies

A family of quantum systems parametrized by the points of a compact space can realize its classical symmetries via a new kind of nontrivial ray representation. We show that this phenomenon in fact occurs for the quantum mechanics of fermions in the presence of background gauge fields, and is responsible for both the nonabelian anomaly and Witten's SU(2) anomaly. This provides a hamiltonian interpretation of anomalies: in the affected theories Gauss' law cannot be implemented. The analysis clearly shows why there are no further obstructions corresponding to higher spheres in configuration space, in agreement with a recent result of Atiyah and Singer.

Eta invariants, charge fractionalization and anomalies

Starting with the observation that the fermionic number operator of a charge fractionalization problem is the (inverse) Mellin transform of the eta invariant of Atiyah, Patodi and Singer, we calculate the eta invariant for odd-dimensional unit spheres. We obtain an interesting interpretation for both the Goldstone-Wilczek mass relation and the eta invariant (in this case, a generalization of the classical conformal invariant of Blaschke et al.). We briefly discuss the possible anomalies of the implied theory by connecting the eta invariant with the spin-index theorem. We show that the known relationship between Abelian and nonabelian anomalies is an interplay between the spin-index theorem and Bott periodicity. Some related questions are also discussed.

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.

Anomalies of Arbitrary Gauge Group and its Reduction Group, Einstein and Lorentz Anomalies

Based upon the properties of the characteristic classes and their Chern-Simons secondary characteristic classes, the “Abelian” anomalies in , the Euler-Heisenberg effective actions in , as well as the non-Abelian anomalies in for arbitrary gauge group and its reduction subgroup have been investigated thoroughly and the application to the gravitational anomalies is made. It is shown that the “Abelian” anomalies of such groups are equal to each other, their Eu1er-Heisenberg actions are also closely related to each, other, and their non-Abelian anomalies are also equivalent if their common generating functional can be taken as a counter-term. For the gravitational anomalies we present the common generating functional for both non-Abelian Einstein and Lorentz anomalies in and show the relationship between them.

Anomalies, Cohomology and Chiern-Simons Cochains

We present a concept of cohomology of the gauge transformations, establish the homomorphic relation between this cohomology group and the Chern-Simons type characteristic class sequence, and analyse their applications to the non-Abelian anomaly, the gauge invariant Wess-Zumino effective action and the Schwinger term etc. We show that the present approach includes faddeev's song's and zumino's approaches.

Non-topological anomalies and Wess-Zumino effective action

The uniqueness of the full non-abelian anomaly, including the terms additional to the usual Bardeen anomaly, is proven within gauge-invariant perturbation theory. The resulting effective Wess-Zumino lagrangian describes both normal and abnormal parity processes. The slope parameter λ+ in Kℓ3 decay and the structure-dependent amplitude in π → eνγ are shown to be uniquely determined by the anomaly.

Non-Abelian Anomaly and Vector Mesons as Dynamical Gauge Bosons of Hidden Local Symmetries

We present general solutions to the Wess-Zumino anomaly equation which incorporate vector mesons as dynamical gauge bosons of the hidden local symmetry in the nonlinear chiral Lagrangian. In contrast to the previous attempts to introduce the vector mesons, our formalism enables one to treat consistently and systematically various processes associated with pseudoscalar mesons (Nambu-Goldsone bosons) and vector mesons (dynamical gauge bosons); it is automatic in this framework that the on-shell amplitudes of photons and pseudoscalar mesons such as π0 →2γ and γ→3 π which are fixed by the low energy theorems, are not affected no matter how the vector mesons participate in those processes. We further show that the “complete vector meson dominance” hypothesis of photon couplings is invalid in either π0 →2γ or γ→3π process.

Decoupling a fermion whose mass is generated by a Yukawa coupling: The general case

The low-energy effective action for a fermion whose mass is generated by a Yukawa coupling to a Higgs field is computed in the limit of infinite fermion mass. A Wess-Zumino term as a function of the Higgs field is discovered. Gauge fields are included, and the low-energy effective action reproduces all the anomalies of the original theory. Our construction naturally leads to a six-dimensional formulation for the non-abelian anomaly.

Anomalies and fermion zero modes on strings and domain walls

the parity anomaly in 2n + 1 dimensions, and the Dirac index density in 2n + 2 dimensions can be understood in terms of the physics of fermion zero modes on strings and domain walls. We show that the Dirac equation possesses chiral zero modes in the presence of strings in 2n +2 dimensions (such as occur in axion theories) or domain walls in 2n + 1 dimensions. We show that the anomalies due to the chiral zero modes are exactly cancelled by anomalies due to the coupling of axion-like fields to the Dirac index density or by anomalies due to the induced topological mass term. Anomalies arise when the quantum-mechanical vacuum functional of a field theory fails to have all the symmetries of the classical lagrangian from which it is derived. Ifthe symmetry in question is a gauge symmetry associated with a dynamical gauge field, the anomaly is intolerable and must be eliminated. The usual method is direct cancellation by the addition of extra fermion species with appropriate quantum numbers. In this paper, we will show that in certain contexts involving defects (i.e. strings and domain walls), anomalies arise which may be compensated by quantum number flows in the higher-dimensional space in which the defect is embedded, rather than cancelled. This phenomenon gives a particularly simple physical interpretation of the recently discovered mathematical connection between chiral anomalies in 2n +2 dimensions, parity anomalies in 2n + l dimensions and gravitational and non-abelian anomalies in 2n dimensions [1-5]. It also suggests some interesting phenomenological possibilities for the axion strings which may have played a role in the development of density perturbations in the early universe

Chiral anomalies and the generalised index theorem

Shows that the generalised Atiyah-Singer index theorem (1968), describes not only the U(1) anomaly but also the non-Abelian anomaly. These anomalies are determined in arbitrary even dimensions without ambiguity of coefficients. The index theorem reveals new kinds of anomalies. The relationship between these anomalies and the topology of Yang-Mills fields is discussed.

The topological meaning of non-abelian anomalies

We show how the non-abelian anomaly for gauge fields coupled to Weyl fermions in 2 n dimensions is related to the non-trivial topology of gauge orbit space. The form of the anomaly and its normalization are shown to follow from a familiar index theorem for a certain (2 n + 2)-dimensional Dirac operator. We are thus able to recover and give topological meaning to a variety of results concerning anomalies in 4- and higher-dimensional theories.