Related papers: Duflo Isomorphism and Chern-Weil Theory
We present a formulation of chiral gauge theories, which admits more general spectra of Dirac operators and reveals considerably more possibilities for the structure of the chiral projections. Our two forms of correlation functions both…
The relative index theorem is proved for general first-order elliptic operators that are complete and coercive at infinity over measured manifolds. This extends the original result by Gromov-Lawson for generalised Dirac operators as well as…
In this paper, we show the existence of a sequence of invariant differential operators on a particular homogeneous model $G/P$ of a Cartan geometry. The first operator in this sequence can be locally identified with the Dirac operator in…
We propose a discretisation scheme based on the Dirac-Kahler formalism (DK) in which the algebraic relations between continuum operators ${\wedge, d, \star}$ are captured by their discrete analogues, allowing the construction of the…
We still extend the large class of Dirac operators decribing massless fermions on the lattice found recently, only requiring that such operators decompose into Weyl operators. After deriving general relations and constructions of operators,…
We review the spectral flow techniques for computing the index of the overlap Dirac operator including results relevant for SUSY Yang-Mills theories. We describe properties of the overlap Dirac operator, and methods to implement it…
In this expository article, we consider first order elliptic differential operators acting on smooth vector bundles over compact manifolds, and certain invariants derived from the analysis of these operators, namely the eta invariant} and…
A Chern-Weil construction for extensions of Lie-Rinehart algebras is introduced. This generalizes the classical Chern-Weil construction in differential geometry and yields characteristic classes for arbitrary extensions of Lie-Rinehart…
Some linear integro-differential operators have old and classical representations as the Dirichlet-to-Neumann operators for linear elliptic equations, such as the 1/2-Laplacian or the generator of the boundary process of a reflected…
Instead of the Ginsparg-Wilson (GW) relation we only require generalized chiral symmetry and show that this results in a larger class of Dirac operators describing massless fermions, which in addition to GW fermions and to the ones proposed…
In this paper we analyze the invariance of the Dirac equation under disformal transformations depending on the propagating spinor field. Using the Weyl-Cartan formalism, we construct a large class of disformal maps between different metric…
First, we review the Dirac operator folklore about basic analytic and geometrical properties of operators of Dirac type on compact manifolds with smooth boundary and on closed partitioned manifolds and show how these properties depend on…
We formulate, for any Lie group G acting isometrically on a manifold M, the general notion of a G-equivariant elliptic operator that is invertible outside of a G-cocompact subset of M. We prove a version of the Rellich lemma for this…
Chern-Weil and Chern-Simons theory extend to certain infinite-rank bundles that appear in mathematical physics. We discuss what is known of the invariant theory of the corresponding infinite-dimensional Lie groups. We use these techniques…
Suppose that $(M,E)$ is a compact contact manifold, and that a compact Lie group $G$ acts on $M$ transverse to the contact distribution $E$. In an earlier paper, we defined a $G$-transversally elliptic Dirac operator $\dirac$, constructed…
A Chern-Simons action written with Christoffel Symbols has a natural gauge symmetry of diffeomorphisms. This Chern-Simons action will induce a Wess-Zumio-Witten model on the boundary of the manifold. If we restrict the diffeomorphisms to…
We construct the double copy of the chiral higher-spin theory. It is a Lorentz invariant theory with the little group spectrum given by the tensor square of the chiral higher-spin theory spectrum. Moreover, its interactions factorise in…
A family of theories which interpolate between vector and chiral Schwinger models is studied on the two--sphere $S^{2}$. The conflict between the loss of gauge invariance and global geometrical properties is solved by introducing a fixed…
We introduce a gauge-theoretic integer lift of the Rohlin invariant of a smooth 4-manifold X with the homology of $S^1 \times S^3$. The invariant has two terms; one is a count of solutions to the Seiberg-Witten equations on X, and the other…
We describe the center of the ring $\Diff(n)$ of $\h$-deformed differential operators of type A. We establish an isomorphism between certain localizations of $\Diff(n)$ and the Weyl algebra $\text{W}_n$ extended by $n$ indeterminates.