相关论文: Lagrangian approach to sheaves of vertex algebras

We study factorization algebras on configuration spaces of points on the curved, colored by elements of the root lattice. We show that the factorization algebra attached to Lusztig's quantum group can be obtained as a direct image of a…

We prove that the extended Khovanov arc algebras are isomorphic to the basic algebras of anti-spherical Hecke categories for maximal parabolics of symmetric groups. We present these algebras by quiver and relations and provide the full…

We consider the extended superconformal algebras of the Knizhnik-Bershadsky type with $W$-algebra like composite operators occurring in the commutation relations, but with generators of conformal dimension 1,$\frac{3}{2}$ and 2, only. These…

Lagrangian multiforms provide a variational framework to describe integrable hierarchies. The case of Lagrangian $1$-forms covers finite-dimensional integrable systems. We use the theory of Lie dialgebras introduced by Semenov-Tian-Shansky…

We study associative multiplications in semi-simple associative algebras over C compatible with the usual one or, in other words, linear deformations of semi-simple associative algebras over C. It turns out that these deformations are in…

Conformal sigma models and WZW models on coset superspaces provide important examples of logarithmic conformal field theories. They possess many applications to problems in string and condensed matter theory. We review recent results and…

We compare the context of Hodge structures with that of vertex algebras of conformal field theory. Vertex algebras appear as the highest weight representations of infinite dimensional Lie algebras. A correspondence between Higgs bundles and…

We construct and study SUSY lattice vertex algebras. As a simple example, we obtain the simple vertex algebra associated to the vertex algebra $V_c(N3)$ of central charge $c=3/2$, as the SUSY lattice vertex algebra associated to…

The universal $2$-parameter vertex algebra $W_{\infty}$ of type $W(2,3,4,\dots)$ serves as a classifying object for vertex algebras of type $W(2,3,\dots,N)$ for some $N$ in the sense that under mild hypothesis, all such vertex algebras…

We give an a priori proof of the known presentations of (that is, completeness of families of relations for) the principal subspaces of all the standard A_1^(1)-modules. These presentations had been used by Capparelli, Lepowsky and Milas…

We investigate a relationship between a particular class of two-dimensional integrable non-linear $\sigma$-models and variations of Hodge structures. Concretely, our aim is to study the classical dynamics of the $\lambda$-deformed $G/G$…

Given a compact oriented manifold of dimension $n$ with a conically smooth stratification, we show that the moduli of $\mathcal{D}(k)$-valued constructible sheaves and the moduli of perverse sheaves are $(2-n)$-shifted Lagrangian. The…

Given an augmentation for a Legendrian surface in a $1$-jet space, $\Lambda \subset J^1(M)$, we explicitly construct an object, $\mathcal{F} \in Sh_{\Lambda}$, of the (derived) category from arXiv:1402.0490 of constructible sheaves on…

We construct a quasi-coherent sheaf of associative algebras which controls a category of $AV$-modules over a smooth quasi-projective variety. We establish a local structure theorem, proving that in \'etale charts these associative algebras…

We associate vertex operator algebras to $(p,q)$-webs of interfaces in the topologically twisted $\mathcal{N}=4$ super Yang-Mills theory. Y-algebras associated to trivalent junctions are identified with truncations of…

Extending our earlier work on PSL(2|2), we explain how to reduce the solution of WZNW models on general type I supergroups to those defined on the bosonic subgroup. The new analysis covers in particular the supergroups GL(M|N) along with…

Here we define a series of associative algebras attached to a vertex operator algebra $V$, called mode transition algebras, showing they reflect both algebraic properties of $V$ and geometric constructions on moduli of curves. One can…

This is a survey on Zariski equisingularity. We recall its definition, main properties, and a variety of applications in Algebraic Geometry and Singularity Theory. In the first part of this survey, we consider Zariski equisingular families…

We have perturbed Wess-Zumino-Witten (WZW) models and also N=(2,2) supersymmetric sigma models on Lie groups by adding a term containing complex structure to their actions. Then, using non-coordinate basis, we have shown that for N=(2,2)…

We calculate the most general terms for arbitrary Lagrangians of twisted chiral superfields in 2D (2,2) supersymmetric theories [1]. The scalar and fermion kinetic terms and interactions are given explicitly. We define a set of twisted…