相关论文: Z_2-reductions of spinor models in two dimensions

We consider the close relation between duality in N=2 SUSY gauge theories and integrable models. Various integrable models ranging from Toda lattices, Calogero models, spinning tops, and spin chains are related to the quantum moduli space…

We write general and explicit equations which solve the supersymmetry transformations with two arbitrary complex-proportional Weyl spinors on $\mathcal{N}=1$ supersymmetric type IIB strings backgrounds with all R-R $F_1$, $F_3$, $F_5$ and…

We generalize Zagiers work on regularized integral to the singular case in the adelic setting. We develop necessary tools of treating various singular cases of regularized triple product formulas, which appear naturally in the work of…

We study d=2, N=(2,2) non-linear sigma-models in (2,2) superspace. By analyzing the most general constraints on a superfield, we show that through an appropriate choice of coordinates, there are no other superfields than chiral, twisted…

Spinor description for the curvatures of $D=5$ Yang-Mills, Rarita-Schwinger and gravitational fields is elaborated. Restrictions imposed on the curvature spinors by the dynamical equations and Bianchi identities are analyzed. In the absence…

Continuing our exploration of maximally supersymmetric gauge theories (MSYM) deformed by higher dimensional operators, in this paper we consider an off-shell approach based on pure spinor superspace and focus on constructing supersymmetric…

In this note we discuss several properties of the Schur index of N=2 superconformal theories in four dimensions. In particular, we study modular properties of this index under SL(2,Z) transformations of its parameters.

Results on symplectic spinors and their higher spin versions, concerning representation theory and cohomology properties are presented. Exterior forms with values in the symplectic spinors are decomposed into irreducible modules including…

We present a method for constructing hierarchies of solutions to $n$-simplex equations by variating the spectral parameter in their Lax representation. We use this method to derive new solutions to the set-theoretical 2- and 3-simplex…

New integral representations for form factors in the two parametric SS model are proposed. Some form factors in the parafermionic sine-Gordon model and in an integrable perturbation of SU(2) coset conformal field theories are…

We study mapping properties of two-dimensional linear integral operators in some weighted spaces with special kernels. The considered spaces are certain variant of Sobolev--Slobodetskii spaces and their generalizations related to Banach…

We consider $N$-wave type equations related to the orthogonal algebras obtained from the generic ones via additional reductions. The first $\mathbb{Z}_2$-reduction is the canonical one. We impose a second $\mathbb{Z}_2$-reduction and…

In this paper we present a general framework to construct integrable $\mathbb{Z}_2^2$-graded extensions of classical, two-dimensional Toda and conformal affine Toda theories. The scheme is applied to define the extended Liouville and…

We transfer the scheme of constructing differential reductions, developed recently for the case of the Manakov-Santini hierarchy, to the general multidimensional case. We consider in more detail the four-dimensional case, connected with the…

A $2n$-dimensional Lax integrable system is proposed by a set of specific spectral problems. It contains Takasaki equations, the self-dual Yang-Mills equations and its integrable hierarchy as examples. An explicit formulation of Darboux…

We introduce spinors, at a level appropriate for an undergraduate or first year graduate course on relativity, astrophysics or particle physics. The treatment assumes very little mathematical knowledge (mainly just vector analysis and some…

Recent progress to construct Dirac operators and spinors on compact quantum groups is discussed. The case $SU_q(2)$ is studied carefully and the relationship between known approaches is explained. New examples are given.

A systematic presentation of spinors in various dimensions is given.

A coupled massive Thirring model of two interacting Dirac spinors in $1+1$ dimensions with fields taking values in a Grassmann algebra is introduced, which is closely related to a SU(1,1) version of the Grassmannian Thirring model also…

The article consists of the Russian and English variants of Ph.D. Thesis in which the answers is given on the following questions: 1. how to construct the spinor formalism for n=6; 2. how to construct the spinor formalism for n=8; 3. how to…