Fermionic representation of the Wess-Zumino term and the chiral Schwinger model

The quantum structure of the chiral Schwinger model is studied by fermionization of the Wess-Zumino field. The model contains a hidden parameter a reflecting the ambiguity in the definition of the gauge anomaly. It is shown that, for the special value a = 2, this chiral model is equivalent to massless QED₂ in the sence that they share the same gauge field and the same (left-handed) chiral fermion. The fermionic representation of the Wess-Zumino term provides a natural way to summarize the current algebras and yields a regularization-independent current-algebraic characterization of the model.     

Modular invariance,chiral anomalies and contact terms

The chiral anomaly in heterotic strings with full and partial modular invariance in D = 2n + 2 dimensions is calculated. The boundary terms which were present in previous calculations are shown to be cancelled in the modular-invariant case by contact terms, which can be obtained by an appropriate analytic continuation. The relation to the low-energy field theory is explained. In theories with partial modular invariance, an expression for the anomaly iis obtained and shown to be non-zero in general.     

Catoptric tadpoles

Fermionic string perturbation theory is known to suffer from an ambiguity in the form of a total derivative in the moduli space. For a class of backgrounds (including R¹⁰, orbifolds and theories with no U(1) factors in gauge group) we show that these ambiguities for the partition function of heterotic string theory at any genus are proportional to massless physical tadpoles in the theory at lower genera and hence vanish in stable vacua. We also find that in R¹⁰ the cosmological constant at a given genus is proportional to the cosmological constant at lower genera. This enables us to give an inductive argument for the vanishing of the cosmological constant in R¹⁰ to all orders in string perturbation theory. We also address the ambiguity and finiteness of n-point functions. Our results indicate that in R¹⁰ the ambiguity can be absorbed by a renormalization of the string coupling constant and the string tension. The expected sources of divergence in the n-point function in arbitrary tachyon-free backgrounds, besides the usual infrared divergences for d ≤ 4, are shown to be proportional to tadpoles of physical massless fields. For type II strings in arbitrary backgrounds, we show by explicit calculations that the ambiguity vanishes at g = 2.     

Logarithmic divergence in four-dimensional string theory

Logarithmic divergences in the one-loop scattering amplitude of the heterotic string compactified on the Z_n-orbifold are investigated. The coefficient of these divergences is shown to be a function of the indices of the representations to which the massless states of the model belong.     

Chiral fermions in stochastic quantization

The simultaneous conservation of chiral and gauge currents in the framework of stochastic quantization is discussed. By means of the stochastic regularization procedure we explicitly compute the axial anomaly for fermions with mass m≠0 and the fictitious time t→∞. However, when m≡0, an ambiguity appears: it turns out that the two limits (m→0, t→∞) do not commute. In this case non-perturbative methods show that the difference between left-handed and right-handed zero modes cancels; therefore no anomaly is present and stochastic regularization is unable to describe chiral theories at finite fictitious time. It is in any case unclear how stochastic quantization can describe a massless fermion at finite t.     

Managing <Emphasis Type="Italic">γ</Emphasis><Subscript>5</Subscript> in Dimensional Regularization II: the Trace with more <Emphasis Type="Italic">γ</Emphasis><Subscript>5</Subscript>’s

In the present paper we evaluate the anomaly for the abelian axial current in a non abelian chiral gauge theory, by using dimensional regularization. This amount to formulate a procedure for managing traces with more than one γ ₅. The suggested procedure obeys Lorentz covariance and cyclicity, at variance with previous approaches (e.g. the celebrated ’t Hooft and Veltman’s where Lorentz is violated). The result of the present paper is a further step forward in the program initiated by a previous work on the traces involving a single γ ₅. The final goal is an unconstrained definition of γ ₅ in dimensional regularization. Here, in the evaluation of the anomaly, we profit of the axial current conservation equation, when radiative corrections are neglected. This kind of tool is not always exploited in field theories with γ ₅, e.g. in the use of dimensional regularization of infrared and collinear divergences.     

Hard pions and axial meson exchange current effects in negative muon capture in deuterium

The contribution of the axial meson exchange current effects to the doublet transition rate in the reaction μ^? +d → 2n+ ν_μ is calculated by using the minimal, chiral and approximately gauge invariant Lagrangian model for the A₁ρπ system. The contribution from the ρ-π weak decay process current usually considered is found to be nearly cancelled by that from the A₁ pole graph which is prescribed by the underlying invariance principles. Correct treatment of the N¹ propagator in the N¹ excitation current of the pion range leads to ≈ 30 % suppression of the N¹ effect.     

Chiral anomaly in a spherical spacetime

We evaluate the chiral anomaly for a gauge theory on Sⁿ in the hyperspherical O(n + 1) covariant formalism using the method of Fujikawa and comment on related aspects.     

Gauge theory ofSU(2) Weyl fermion: Is it consistent?

Gauge theory ofSU(2) Weyl fermions was alleged by Witten to be inconsistent due to global anomaly. Evidences of inconsistency were also reported from contradictions between the anomalousU(1) symmetry and the fact that theSU(2) group is free of local anomaly. Here we show how the zero modes of Dirac operator, ignored by the authors of these arguments, play a decisive role and saveSU(2) Weyl fermions from inconsistency in each case. The symmetric chiral current, obtained by adding the Chern-Simons current to the fermionic chiral current, fails to be conserved precisely due to the contributions of zero modes to the ABJ anomaly equation. The Jacobian of the fermion measure under rigid chiralU(1) transformation is, however, guaranteed to be trivial by the Atiyah-Singer index theorem. Finally, a zero mode is the point of bifurcation of eigenvalue trajectory in the homotopy space. In its neighbourhood the hypothesis of adiabaticity made by Witten breaks down due to violent oscillations between levels, which makes his allegation of global anomaly untenable.     

Singularity structure of massless QCD at finite temperature

A complete relativistic calculation to first order in the strong coupling constantα _s is presented for deep inelastic scattering of leptons off a heat bath of quarks and gluons. The singularity structure is studied and the cancellation of all collinear and infrared divergences is proven. It is shown that it is necessary to include all processes of a given order (i.e. not only the gluon emission and absorption as usually stated). We show that for non-equilibriumn _F andn _B distributions the collinear singularities do not cancel.     

Coleman-Weinberg symmetry breaking in the chiral SU(n) × SU(n) linear σ model

The onset of symmetry breaking in the chiral SU(n) × SU(n) linear σ model is investigated. It is shown that the model possesses no stable fixed points in d = 4 ? ? dimensions and that the chiral symmetry of the theory can be broken via the CW mechanism when d = 4. The implications of these results are discussed.     

Gravitational anomalies

It is shown that in certain parity-violating theories in 4k+2 dimensions, general covariance is spoiled by anomalies at the one-loop level. This occurs when Weyl fermions of $\text{spin}\text{-}\text{1}\text{2}\text{or}\text{-3}\text{2}$ or self-dual antisymmetric tensor fields are coupled to gravity. (For Dirac fermions there is no trouble.) The conditions for anomaly cancellation between fields of different spin is investigated. In six dimensions this occurs in certain theories with a fairly elaborate field content. In ten dimensions there is a unique theory with anomaly cancellation between fields of different spin. It is the chiral n = 2 supergravity theory, which is the low-energy limit of one of the superstring theories. Beyond ten dimensions there is no way to cancel anomalies between fields of different spin.     

Virtual photons in chiral perturbation theory

In the framework of chiral perturbation theory virtual photons are included. We calculate the divergences of the generating functional to one loop and determine the structure of the local action that incorporates the counterterms which cancel the divergences. As an application we discuss the corrections to Dashen's theorem at order e²M_q.     

Global gravitational anomalies from perturbative chiral anomalies

The relation between (4k ? 2)-dimensional global gravitational anomalies and perturbative chiral anomalies in 4k dimensions is clarified using an open space generalization of the Atiyah-Patodi-Singer index theorem. These anomalies are then reduced to a chiral anomaly in a two-dimensional Schwinger model. It is argued that “all” anomalies can be similarly reduced.     

The dominance of low-energy contributions to the Casimir energy in the chiral bag model

The smearing of the discrete mode sums leading to the Casimir energy and other vacuum quark contributions to baryon observables in the chiral bag model is shown to give smooth densities dominated by low-energy contributions. This observation provides support for methods previously adopted for the elimination of divergences in such calculations and leads to significant numerical improvements over standard mode sum techniques.     

Low temperature properties of the metallic antiferromagnet ErZn12

The metallic antiferromagnet ErZn₁₂ orders magnetically at 2·76°K. We report measurements of the susceptibility, magnetisation, resistivity and specific heat of polycrystalline specimens of it in the vicinity of the magnetically ordered regime. We find evidence for a metamagnetic or spin-flop transition in fields of 3–7KOe. The resistivity increases monotonically from low temperature to the Néel point and has a power-law dependence on temperature of Tⁿ, where n～6·5. The specific heat shows a lambda anomaly at the Néel point and the divergences which appear above and below it are compared with those reported previously in the resistivity. The magnetic entropy indicates that the ordering process involves only one crystal-field doublet.     

Nonlocality for graph states

The possibility of preparing two-photon entangled states encoding three or more qubits in each photon leads to the following problem: If n quabits were distributed between two parties, which quantum pure states and qubit distributions would allow all-versus-nothing (or Greenberger-Horne-Zeilinger-like) proofs of Bell’s theorem using only single-qubit measurements? We show a necessary and sufficient condition for the existence of these proofs and provide all existing proofs up to n = 7 qubits. On the other hand, the possibility of preparing n-photon n-qubit graph states leads to the following problem: If n qubits were distributed between n parties, which would be the optimal Bell inequalities? We show all optimal n-party Bell inequalities for the perfect correlations of any graph state of n < 6 qubits. Optimal means that the ratio between the quantum violation and the bound for local hidden-variable theories is the maximum over all possible combinations of perfect correlations. This implies that the required detection efficiencies for loophole-free Bell tests are minimal.     

Chiral symmetry breakdown,anomaly, and the PCAC relation on a lattice

Lattice fermion formulation is investigated using a solvable model which resembles quantum chromodynamics. CP₂^N?1 models with quarks are formulated on a lattice. For dynamical quarks, a generalized formulation of the Wilson and the Osterwalder-Seiler lattice fermion is used. In the $\text{1}\text{N}$ expansion, the spontaneous breakdown of chiral symmetry (which is softly broken by the quark mass) apparently occurs in this model, and the “pion” mass is calculated. From the above results, it is shown that the above lattice fermion formulations have the desired continuum limit. The axial-vector current is investigated and it is proved that the usual anomaly appears in the continuum limit and the PCAC relation is satisfied.     

Infrared properties of two-loop,initial state spectator interactions in the Drell-Yan process

We use the light-cone axial gauge of proper-time ordered perturbation theory and study the soft-IR properties of the two-loop virtuals' diagrams considered by Bodwin, Brodsky and Lepage for ππ → μ⁺μ^- + X. It is shown that although the systematic summation over all possible spectator interactions removes the outside soft-IR divergences in the non-overlapping ladder Glauber diagrams, unphysical inside soft-IR divergences persist. So, in the light-cone axial gauge the on-shell Glauber region is not a gauge invariant concept which can be physically isolated from radiative corrections which non-trivially involve other diagrammatic regions. Due to gauge invariance it can be potentially misleading in eikonal phenomenologies based on perturbative QCD to assume an ad hoc inside soft-IR cutoff in analyzing possible non-abelian effects in multiple scatterings involving spectators.     

An effective lagrangian with no U(1) problem in CPn−1 models and QCD

We write an effective lagrangian which gives two-point Green's functions satisfying the anomalous Ward identities for the U(1) axial vector current with a singlet particle that has a non-vanishing mass in the chiral limit. We show that the mechanism that has been postulated by Witten and Veneziano for solving the U(1) problem in the framework of the 1/n expansion in QCD is fully active in the two-dimensional CP^n? model where the 1/n expansion can be explicitly performed.