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.
The nonabelian global chiral symmetries of the two-dimensional N flavour massless Schwinger model are realised through bosonisation and a vertex operator construction.
We study $(2,2)$ and $(4,4)$ supersymmetric theories with superspace higher derivatives in two dimensions. A characteristic feature of these models is that they have several different vacua, some of which break supersymmetry. Depending on the vacuum,
the equations of motion describe different propagating degrees of freedom. Various examples are presented which illustrate their generic properties. As a by-product we see that these new vacua give a dynamical way of generating non-linear realizations. In particular, our 2D $(4,4)$ example is the dimensional reduction of a 4D $N=2$ model, and gives a new way for the spontaneous breaking of extended supersymmetry.
We explore holographic entanglement entropy for Minkowski spacetime in three and four dimensions. Under some general assumptions on the putative holographic dual, the entanglement entropy associated to a special class of subregions can be computed us
ing an analog of the Ryu-Takayanagi formula. We refine the existing prescription in three dimensions and propose a generalization to four dimensions. Under reasonable assumptions on the holographic stress tensor, we show that the first law of entanglement is equivalent to the gravitational equations of motion in the bulk, linearized around Minkowski spacetime.