Related papers: A note on half-integer irregular representations o…

We explore the proposal that the six-dimensional (2,0) theory on the Riemann surface with irregular punctures leads to a four-dimensional gauge theory coupled to the isolated N=2 superconformal theories of Argyres-Douglas type, and to…

We study anomalies of discrete internal global symmetry $G$ in two-dimensional rational conformal field theories based on twisted torus partition functions. The anomaly of $G$ can be seen from the noncommutativity of two symmetry lines…

Recently Kazama and Yokoi (arXiv:0801.1561 [hep-th]) have used a phase-space method to study the Virasoro algebra of type IIB superstring theory in the maximally supersymmetric R-R plane wave background in a semi-light-cone gauge. Two types…

We study the bosonic VOA associated with the 3D $\mathcal{N}=4$ abelian linear quiver gauge theories arising from compactifying 4D $\mathcal{N}=2$ Argyres-Douglas theories of $(A_1,A_{2n-1})$ and $(A_1,D_{2n})$ types. These VOAs are…

We discuss an application of the method of the angular quantization to reconstruction of form-factors of local fields in massive integrable models. The general formalism is illustrated with examples of the Klein-Gordon, sinh-Gordon and…

For an arbitrary calibrated Frobenius manifold, we construct an infinite dimensional Lie algebra, called the Virasoro-like algebra, which is a deformation of the Virasoro algebra of the Frobenius manifold. By using the Virasoro-like algebra…

We introduce fusion algebras with not necessarily positive structure constants and without identity element. We prove that they are semisimple when tensored with $\mathbb{C}$ and that their characters satisfy orthogonality relations. Then…

Cluster coordinates for a large class of Argyres-Douglas and asymptotical free theories are constructed using network on bordered Riemann surface. Such N = 2 theories are engineered using six dimensional (2, 0) theory on Riemann surface…

Let $\mathfrak{g}$ be a simple Lie algebra. We study 1/2-BPS Wilson loops of supersymmetric 5d $\mathfrak{g}$-type quiver gauge theories on a circle, in a non-trivial instanton background. The Wilson loops are codimension 4 defects of the…

This paper is a continuation of arXiv:1405.1707. We present certain new applications and generalizations of the free field realization of the twisted Heisenberg-Virasoro algebra ${\mathcal H}$ at level zero. We find explicit formulas for…

A conformal restriction system is a commutative, associative, unital algebra equipped with a representation of the groupoid of univalent conformal maps on connected open sets of the Riemann sphere, and a family of linear functionals on…

A 2D- fractional supersymmetry theory is algebraically constructed. The Lagrangian is derived using an adapted superspace including, in addition to a scalar field, two fields with spins 1/3,2/3. This theory turns out to be a rational…

We approach the question of complexification of the diffeomorphism group of the circle by considering real-analytic maps from the circle into the punctured complex plane with winding number +1. Such complex deformations form an…

We demonstrate that any scale-invariant mechanics of one variable exhibits not only 0+1 conformal symmetry, but also the symmetries of a full Virasoro algebra. We discuss the implications for the adS/CFT correspondence.

We study natural partial normalization spaces of Coxeter arrangements and discriminants and relate their geometry to representation theory. The underlying ring structures arise from Dubrovin's Frobenius manifold structure which is lifted…

We make use of O(2r+1) spinning particle models to construct linearized higher-spin curvatures in (A)dS spaces for fields of arbitrary half-integer spin propagating in a space of arbitrary (even) dimension: the field potentials, whose…

We solve the problem of constructing a genus-zero full conformal field theory (a conformal field theory on genus-zero Riemann surfaces containing both chiral and antichiral parts) from representations of a simple vertex operator algebra…

In this first of two papers, we explain in detail the simplest example of a broader set of relations between apparently very different theories. Our example relates $\mathfrak{su}(2)$ $\mathcal{N}=4$ super Yang-Mills (SYM) to a theory we…

We give a mathematical interpretation of the dualities between type $A$ Argyres-Douglas theories recently obtained by Beem, Martone, Sacchi, Singh and Stedman, building on work of Xie. Using the fact that, via the wild nonabelian Hodge…

We develop dualities for complete perfect distributive quasi relation algebras and complete perfect distributive involutive FL-algebras. The duals are partially ordered frames with additional structure. These frames are analogous to the…