Related papers: Chiral differential operators on abelian varieties
We present affine Lie algebras generated by the supercovariant derivatives and the supersymmetry generators for the left and right moving modes in the doubled space. Chirality is manifest in our doubled space as well as the T-duality…
We propose a notion of algebra of {\it twisted} chiral differential operators over algebraic manifolds with vanishing 1st Pontrjagin class. We show that such algebras possess families of modules depending on infinitely many complex…
We study the Morita equivalence for fermion theories on noncommutative two-tori. For rational values of the $\theta$ parameter (in appropriate units) we show the equivalence between an abelian noncommutative fermion theory and a nonabelian…
We state and prove an analog of the Schur-Weyl duality for a quotient of the classical $2$-toroidal Lie algebra of type $A$. We then provide a method to extend this duality to the $m$-toroidal case, $m > 2$.
We introduce the notion of a variety (or more generally a motive) of CM-type which generalises the well known notion of abelian variety of CM-type. Just as in that particular case it will turn out that the cohomology of the variety is…
We correct the proof of the main result of an earlier paper, parametrizing orbital varieties in a complex simple Lie algebra of type $B$ or $C$ in terms of domino tableaux and showing how to compute the orbital variety attached to an…
Chiral gauge groups acting on a lattice fermion field are constructed such that all fermion modes (doublers) have the same charge. Details are given for an abelian axial gauge group within a perturbative framework. An action based on this…
Through examples, we illustrate how to compute differential operators on a quotient of an affine semigroup ring by a radical monomial ideal, when working over an algebraically closed field of characteristic 0.
We construct a new equivariant cohomology theory for a certain class of differential vertex algebras, which we call the chiral equivariant cohomology. A principal example of a differential vertex algebra in this class is the chiral de Rham…
We present a Lagrangian formulation for the general modified chiral model. We use it to discuss the Hamiltonian formalism for this model and to derive the commutation relations for the chiral field. We look at some explicit examples and…
Some key features of the symmetries of the Schr\"odinger equation that are common to a much broader class of dynamical systems (some under construction) are illustrated. I discuss the algebra/superalgebra duality involving first and…
We discuss a discrete analogue of the Dirac-K\"{a}hler equation in which chiral properties of the continual counterpart are captured. We pay special attention to a discrete Hodge star operator. To build one a combinatorial construction of…
We classify all non-invertible Kramers-Wannier duality defects in the $E_8$ lattice Vertex Operator Algebra (i.e. the chiral $(E_8)_1$ WZW model) coming from $\mathbb{Z}_m$ symmetries. We illustrate how these defects are systematically…
A general way of interpreting odd dimensional models as a doublet of chiral models is discussed. Based on the equations of motion this dual composition is illustrated. Examples from quantum mechanics, field theory and gravity are…
We study limiting cases of the two known integrable chiral-type models with tree-dimensional configuration space. One of the initial models is the non-Abelian Toda $A_2^{(1)}$ model and the other was found by means of the symmetry approach…
The space of local operators in the SU(2) invariant Thirring model (SU(2) ITM) is studied by the form factor bootstrap method. By constructing sets of form factors explicitly we define a susbspace of operators which has the same character…
Differentiations of operator algebras over non-archimedean spherically complete fields are investigated. Theorems about a differentiation being internal are demonstrated.
The space of abelian functions of a principally polarized abelian variety J is studied as a module over the ring D of global holomorphic differential operators on J. We construct a D-free resolution in case the theta divisor is…
We match a few non chiral operators in the electric and magnetic descriptions of SQCD, suggesting the first evidence of electric-magnetic duality outside the chiral ring. Algebraically, these non chiral operators are a module of the chiral…
We consider the asymmetric orbifold that is obtained by acting with T-duality on a 4-torus, together with a shift along an extra circle. The chiral algebra of the resulting theory has non-trivial outer automorphisms that act as permutations…