Related papers: Chiral differential operators on abelian varieties
We develop a systematic way for constructing bispectral algebras of commuting ordinary differential operators of any rank $N$. It combines and unifies the ideas of Duistermaat-Gr\"unbaum and Wilson. Our construction is completely…
In the theory of species, differential as well as integral operators are known to arise in a natural way. In this paper, we shall prove that they precisely fit together in the algebraic framework of integro-differential rings, which are…
The operator solution of the anomalous chiral Schwinger model is discussed on the basis of the general principles of Wightman field theory. Some basic structural properties of the model are analyzed taking a careful control on the Hilbert…
The work is devoted to the variety of $2$-dimensional algebras over an algebraically closed field. Firstly, we classify such algebras modulo isomorphism. Then we describe the degenerations and the closures of principal algebra series in the…
Four-dimensional N=2 superconformal field theories have families of protected correlation functions that possess the structure of two-dimensional chiral algebras. In this paper, we explore the chiral algebras that arise in this manner in…
The existence of an infinite set of conserved currents in completely integrable classical models, including chiral and Toda models as well as the KP and self-dual Yang-Mills equations, is traced back to a simple construction of an infinite…
The classical radial part formula for the invariant differential operators and the K-invariant functions on a Riemannian symmetric space G/K is generalized to some non-invariant cases by use of Cherednik operators and a graded Hecke algebra…
The aim of this paper is to correct a mistake in earlier work on the conformal invariance of Rarita-Schwinger operators and use the method of correction to develop properties of some conformally invariant operators in the Rarita-Schwinger…
We derive the current algebra of supersymmetric principal chiral models with a Wess-Zumino term. At the critical point one obtains two commuting super Kac-Moody algebra as expected, but in general there are intertwining fields connecting…
Lie algebra valued equations translating the integrability of a general two-dimensional Wess-Zumino-Witten model are given. We found simple solutions to these equations and identified three types of new integrable non-linear sigma models.…
We solve the problem of constructing all chiral genus-one correlation functions from chiral genus-zero correlation functions associated to a vertex operator algebra satisfying the following conditions: (i) the weight of any nonzero…
A difference operator on an associative algebra is an algebraic abstraction of the forward and backward difference operators. In this paper, we first introduce difference operators on associative $2$-algebras and consider the category of…
Anomalous sector of chiral Lagrangian is calculated in a gauge invariant, nonlocal, dynamical quark model. The Wess-Zumino term is proved coming from two kinds of sources, one is independent on and another dependent on dynamical quark self…
We show that the smooth theta divisors of general principally polarised abelian varieties can be chosen as irreducible algebraic representatives of the coefficients of the Chern-Dold character in complex cobordisms and describe the action…
We study the approximation of chiral quark models with simpler models, obtained via gradient expansion. The resulting Lagrangian of the type of the linear sigma-model contains, at the lowest level, an additional term with two derivatives.…
In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to…
This is an overview on the {source operator method} which leads to the construction of symmetry breaking differential operators (SBDO) in the context of tensor product of two principals series representations for the conformal group of a…
We consider correlation functions for the Wess-Zumino-Witten model on the torus with the insertion of a Cartan element; mathematically this means that we consider the function of the form $F=\Tr (\Phi_1 (z_1)\ldots \Phi_n…
Let A be an abelian variety over a number field F with End(A/F) commutative. Let S be a subgroup of A(F) and let x be a point of A(F). Suppose that for almost all places v of F the reduction of x modulo v lies in the reduction of S modulo…
Certain perturbative aspects of two-dimensional sigma models with (0,2) supersymmetry are investigated. The main goal is to understand in physical terms how the mathematical theory of ``chiral differential operators'' is related to sigma…