Related papers: A note on half-integer irregular representations o…
We classify the self-dual (or holomorphic) vertex operator superalgebras of central charge 24, or in physics parlance the purely left-moving, fermionic 2-dimensional conformal field theories with just one primary field. There are exactly…
We present an holographical soft wall model which is able to reproduce not only Regge spectra for hadrons with arbitrary integer spin, but also with spin 1/2 and 3/2, and with an arbitrary number of constituents. The model includes the…
We give a proof of the recursive formula on the norm of Whittaker vector of the deformed Virasoro algebra, which is an analog of the one for the Virasoro Lie algebra proposed by Al. Zamolodchikov. Our formula gives a proof of the pure SU(2)…
We classify semisimple left module categories over the representation category of a type A quantum group whose fusion rules arise from the maximal torus. The classification is connected to equivariant Poisson structures on compact full flag…
We propose a simple approach to formal deformations of associative algebras. It exploits the machinery of multiplicative coresolutions of an associative algebra A in the category of A-bimodules. Specifically, we show that certain…
We construct the AdS$_5$ holographic duals to all non-Lagrangian 4d $\mathcal{N}=2$ superconformal field theories of Argyres--Douglas type, namely, $\mathcal{D}_p^{\,b}(G)$, arising from class $\mathcal{S}$ of classical type involving…
The boundary charges which constitute the Virasoro algebra in 2+1 dimensional anti-de Sitter gravity are derived by way of Noether theorem and diffeomorphic invariance. It shows that the boundary charges under discussion recently exhaust…
We define a class of $A_\infty$-algebras that are obtained by deformations of higher spin symmetries. While higher spin symmetries of a free CFT form an associative algebra, the slightly broken higher spin symmetries give rise to a minimal…
In this paper, we study Virasoro vertex algebras and affine vertex algebras over a general field of characteristic $p>2$. More specifically, we study certain quotients of the universal Virasoro and affine vertex algebras by ideals related…
Families of vertex algebras associated to nilpotent elements of simply-laced Lie algebras are constructed. These algebras are close cousins of logarithmic W-algebras of Feigin and Tipunin and they are also obtained as modifications of…
In conformal field theory, the semigroup of annuli with boundary parametrization plays a special role, in that it generates the whole algebra of local conformal symmetries, the so-called Virasoro algebra. The subgroup of elements…
In this paper expressions are given for the bulk and boundary structure constants of D-series Virasoro minimal models on the upper half plane. It is the continuation of an earlier work on the A-series. The solution for the boundary theory…
In this paper we continue to explore the connection between tensor algebras and displacement structure. We focus on recursive orthonormalization and we develop an analogue of the Szego type theory of orthogonal polynomials in the unit…
We suggest a (conjectural) construction of a basis in the plus part of the affine Lie algebra of type ADE indexed by irreducible components of certain quiver varieties. This construction is closely related to a string-theoretic construction…
The goal of this paper is to study the representation theory of a classical infinite-dimensional Lie algebra - the Lie algebra of vector fields on an N-dimensional torus for N > 1. The case N=1 gives a famous Virasoro algebra (or its…
In this work, we introduce Urod algebras associated to simply-laced Lie algebras as well as the concept of translation of W-algebras. Both results are achieved by showing that the quantum Hamiltonian reduction commutes with tensoring with…
This thesis is divided into two parts. In the first part we study completely integrable systems, and their underlying structures, in detail. We study their deformation theory and the different equivalence relations surrounding it. We…
$q,t$-deformed matrix models give rise to representations of the deformed Virasoro algebra and more generally of the quantum toroidal $\mathfrak{gl}_1$ algebra. These representations are described in terms of finite difference equations…
We investigate modular embeddings for semi-arithmetic Fuchsian groups. First we prove some purely algebro-geometric or even topological criteria for a regular map from a smooth complex curve to a quaternionic Shimura variety to be covered…
We study field theories in two spacetime dimensions invariant under a chiral scaling symmetry that acts only on right-movers. The local symmetries include one copy of the Virasoro algebra and a U(1) current algebra. This differs from the 2d…