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Register a new userCovariant Schwinger terms
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We evaluate the gravitational Schwinger terms for the specific two-dimensional model of Weyl fermions in a gravitational background field using a technique introduced by Kallen and find a relation which connects the Schwinger terms with the linearized gravitational anomalies.
We discuss 2-cocycles of the Lie algebra $Map(M^3;g)$ of smooth, compactly supported maps on 3-dimensional manifolds $M^3$ with values in a compact, semi-simple Lie algebra $g$. We show by explicit calculation that the Mickelsson-Faddeev-Shatashvili cocycle $f{ii}{24pi^2}inttrac{Accr{dd X}{dd Y}}$ is cohomologous to the one obtained from the cocycle given by Mickelsson and Rajeev for an abstract Lie algebra $gz$ of Hilbert space operators modeled on a Schatten class in which $Map(M^3;g)$ can be naturally embedded. This completes a rigorous field theory derivation of the former cocycle as Schwinger term in the anomalous Gauss law commutators in chiral QCD(3+1) in an operator framework. The calculation also makes explicit a direct relation of Connes non-commutative geometry to (3+1)-dimensional gauge theory and motivates a novel calculus generalizing integration of $g$-valued forms on 3-dimensional manifolds to the non-commutative case.
We construct a manifestly covariant differential Noether charge for theories with Chern-Simons terms in higher dimensional spacetimes. This is in contrast to Tachikawas extension of the standard Lee-Iyer-Wald formalism which results in a non-covariant differential Noether charge for Chern-Simons terms. On a bifurcation surface, our differential Noether charge integrates to the Wald-like entropy formula proposed by Tachikawa in arXiv:hep-th/0611141.
In this work we explore the applicability of a special gluon mass generating mechanism in the context of the linear covariant gauges. In particular, the implementation of the Schwinger mechanism in pure Yang-Mills theories hinges crucially on the inclusion of massless bound-state excitations in the fundamental nonperturbative vertices of the theory. The dynamical formation of such excitations is controlled by a homogeneous linear Bethe-Salpeter equation, whose nontrivial solutions have been studied only in the Landau gauge. Here, the form of this integral equation is derived for general values of the gauge-fixing parameter, under a number of simplifying assumptions that reduce the degree of technical complexity. The kernel of this equation consists of fully-dressed gluon propagators, for which recent lattice data are used as input, and of three-gluon vertices dressed by a single form factor, which is modelled by means of certain physically motivated Ansatze. The gauge-dependent terms contributing to this kernel impose considerable restrictions on the infrared behavior of the vertex form factor; specifically, only infrared finite Ansatze are compatible with the existence of nontrivial solutions. When such Ansatze are employed, the numerical study of the integral equation reveals a continuity in the type of solutions as one varies the gauge-fixing parameter, indicating a smooth departure from the Landau gauge. Instead, the logarithmically divergent form factor displaying the characteristic zero crossing, while perfectly consistent in the Landau gauge, has to undergo a dramatic qualitative transformation away from it, in order to yield acceptable solutions. The possible implications of these results are briefly discussed.
We report an analysis of the octet baryon masses using the covariant baryon chiral perturbation theory up to next-to-next-to-next-to-leading order with and without the virtual decuplet contributions. Particular attention is paid to the finite-volume corrections and the finite lattice spacing effects on the baryon masses. A reasonable description of all the publicly available $n_f=2+1$ lattice QCD data is achieved.Utilyzing the Feynman-Hellmann theorem, we determine the nucleon sigma terms as $sigma_{pi N}=55(1)(4)$ MeV and $sigma_{sN}=27(27)(4)$ MeV.
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