Related papers: Virasoro irregular conformal block and beta deform…

Whether the neutrino mass ordering is normal or inverted remains an experimentally open issue in neutrino physics. The knowledge of neutrino mass ordering has great importance for neutrinoless double-beta ($ 0\nu\beta\beta$) decay…

We construct long sequences of braids that are descending with respect to the standard order of braids (``Dehornoy order''), and we deduce that, contrary to all usual algebraic properties of braids, certain simple combinatorial statements…

We derive an explicit expression for the $1/c$ contribution to the Virasoro blocks in 2D CFT in the limit of large $c$ with fixed values of the operators' dimensions. We follow the direct approach of orthonormalising, at order $1/c$, the…

We study six-point correlation functions in two dimensional conformal field theory, where the six operators are grouped in pairs with equal conformal dimension. Assuming large central charge $c$ and a sparse spectrum, the leading…

We introduce FA-matrices for computing ranks of vector bundles of coinvariants and conformal blocks associated with modules over vertex operator algebras on the moduli space of stable pointed curves, unifying the notions of fusion and…

We consider a deformation of Kerov character polynomials, linked to Jack symmetric functions. It has been introduced recently by M. Lassalle, who formulated several conjectures on these objects, suggesting some underlying combinatorics. We…

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)…

In this work, we investigate how the marginal beta deformation of the ${N}=4$ super-Yang-Mills theory manifests within the context of the topological B-model in the twistor space $\mathbb{CP}^{3|4}$. We begin by identifying the beta…

We consider the equations, arising as the conformal invariance conditions of the perturbed curved beta-gamma system. These equations have the physical meaning of Einstein equations with a B-field and a dilaton on a hermitian manifold, where…

We discuss some physical consequences of the resurgent structure of Painleve equations and their related conformal block expansions. The resurgent structure of Painleve equations is particularly transparent when expressed in terms of…

A quantum deformation of the Virasoro algebra is defined. The Kac determinants at arbitrary levels are conjectured. We construct a bosonic realization of the quantum deformed Virasoro algebra. Singular vectors are expressed by the Macdonald…

Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to…

We revisit the construction of the 2d conformal blocks of primary operator four-point functions as bilocal vertex operator correlators. We find an additional interpretation as a path integral over the reparametrizations of an intermediate…

This paper focuses on a conformal block with rank $\frac{3}{2}$ irregular singularity which corresponds to the prepotential of the ${\cal H}_1$ Argyres-Douglas theory in $\Omega$ background. We derive this irregular conformal block using…

What is the connection of random matrices with integrable systems? Is this connection really useful? The answer to these questions leads to a new and unifying approach to the theory of random matrices. Introducing an appropriate time…

We explore how the combinatorial arrangement of prescribed zeros in a matrix affects the possible eigenvalues that the matrix can obtain. We demonstrate that there are inertially arbitrary patterns having a digraph with no 2-cycle, unlike…

We study the class of neutrino mass matrices with a dominant block but unspecified O(1) coefficients, and scan the possible models by the help of random number generators. We discuss which are the most common expectations in dependence of…

We consider mixed type multiple orthogonal polynomials associated with a system of weight functions consisting of two vectors. One vector is defined in terms of scaled modified Bessel function of the first kind $I_\mu$ and $I_{\mu+1}$, the…

This paper is based on my presentation at RIMS workshop on "Theory of Integrable Systems and Its Applications in Various Fields" held in Kyoto on 19--21, August 2015. The aim of the present paper is to give a short account of recent studies…

We reconstruct the neutrino mass matrix in flavor basis, in the case of inverted mass hierarchy (ordering), using all available experimental data on neutrino masses and oscillations. We analyze the dependence of the matrix elements m_{alpha…