Related papers: Chiral differential operators on abelian varieties
We study duality properties of actions for chiral boson fields in various space-time dimensions using D=2 and D=6 cases as examples. As a result we get dual covariant formulations of chiral bosons.
We extend the Altmann-Hausen presentation of normal affine algebraic C-varieties endowed with effective torus actions to the real setting. In particular, we focus on actions of quasi-split real tori, in which case we obtain a simpler…
It is shown how a chiral Wess-Zumino-Witten theory with globally defined vertex operators and a one-to-one correspondence between fields and states can be constructed. The Hilbert space of this theory is the direct sum of tensor products of…
We consider the chiral anomaly for systems with a wide class of Hermitian Dirac operators ${Q}$ in 4D Euclidean spacetime. We suppose that $ Q$ is not necessarily linear in derivatives and also that it contains a coordinate inhomogeneity…
We generalize the linear sigma model in order to develop a chiral-invariant model of nuclear structure. The model is natural, and contains not only the usual sigma meson which is the chiral partner of the pion but also a new chiral-singlet…
We study the complex symmetric structure of weighted composition--differentiation operators of order $n $ on the weighted Bergman spaces $A_{\alpha}^2$ with respect to some conjugations. Then we provide some examples of these operators.
We correct the proof of the main result in an earlier paper, showing how to parametrize orbital varieties in a complex simple Lie algebra of type $D$ in terms of domino tableaux and showing how to compute variety attached to any element of…
This is the written version of a series of lectures reviewing the basics of duality as applied to p-forms and sigma-models. The ideas are introduced by way of worked examples, often quite detailed. Our approach is very pedestrian and the…
We Investigate two types of dual identities for Riemann fractional sums and differences. The first type relates nabla and delta type fractional sums and differences. The second type represented by the Q-operator relates left and right…
In this paper we look at a sigma model based on the (4, 4) twisted chiral multiplet [3]. It admits two geometric descriptions: The ususal bi-quaternionic geometry on the tangent space and a new geometry involving two Yano F-structures on a…
We show for an affine variety $X$, the derived category of quasi-coherent $D$-modules is equivalent to the category of DG modules over an explicit DG algebra, whose zeroth cohomology is the ring of Grothendieck differential operators…
The operators of fractional calculus come in many different types, which can be categorised into general classes according to their nature and properties. We conduct a formal study of the class known as weighted fractional calculus and its…
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…
This paper will initiate a study on the class of complex symmetric operators acting between two different Hilbert space. Among other things, we compute the closure of CSO with respect to the several topologies.
Given a smooth proper morphism $f\colon X\rightarrow S$, we introduce a certain derived category where morphisms are permitted to be $\mathcal{O}_S$-linear differential operators. We then prove a generalisation of Serre duality that applies…
Conformal algebra is an axiomatic description of the operator product expansion (or rather its Fourier transform) of chiral fields in a conformal field theory. This is a review of recent developments in the subject.
In this paper we introduce the conformal fractional Dirac operator and its associated fractional spinorial Yamabe problem. We also present a Caffarelli-Silvestre type extension for this fractional operator, allowing us to express it as a…
We prove a conjecture by Kawaguchi-Silverman on arithmetic and dynamical degrees, for self-morphisms of semi-abelian varieties. Moreover, we determine the set of the arithmetic degrees of orbits and the (first) dynamical degrees of…
Elaborating on previous work (hep-th/0605211, hep-th/0611247), we show how the linear and nonlinear chiral multiplets of N=4 supersymmetric mechanics with the off-shell content (2,4,2) can be obtained by gauging three distinct two-parameter…
We study natural differential operators transforming two tensor fields into a tensor field. First, it is proved that all bilinear operators are of order one, and then we give the full classification of such operators in several concrete…