相关论文: Remarks on irregular conformal blocks and Painlev\…

We develop the theory of irregular conformal blocks of the Virasoro algebra. In previous studies, expansions of irregular conformal blocks at regular singular points were obtained as degeneration limits of regular conformal blocks; however,…

We construct degeneration limits of vertex operators for the Virasoro algebra. Our method relies on the rearranged expansion of compositions of vertex operators together with their integral representations. Using this framework, we obtain a…

We prove a Fredholm determinant and short-distance series representation of the Painlev\'e V tau function $\tau(t)$ associated to generic monodromy data. Using a relation of $\tau(t)$ to two different types of irregular $c=1$ Virasoro…

We present a new systematic way to evaluate the classical limit of the Virasoro irregular conformal block for arbitrary rank n based on the irregular partition function. In addition, we prove that the classical irregular conformal block has…

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…

In recent years, the Fourier series (Zak transform) structure of the Painlev\'e I tau function has emerged in multiple contexts. Its main building block admits several conjectural interpretations, such as the partition function of an…

Although irregular vectors for the Virasoro algebra are widely used in modern mathematical physics, a rigorous existence and uniqueness theorem in arbitrary rank has not been available in the literature. In this paper, we develop an…

We construct the free field representation of irregular vertex operators of arbitrary rank which generates simultaneous eigenstates of positive modes of Virasoro and W symmetry generators. The irregular vertex operators turn out to be the…

The short-distance expansion of the tau function of the radial sine-Gordon/Painlev\'e III equation is given by a convergent series which involves irregular $c=1$ conformal blocks and possesses certain periodicity properties with respect to…

We study irregular states of rank-two and three in Liouville theory, based on an ansatz proposed by D. Gaiotto and J. Teschner. Using these irregular states, we evaluate asymptotic expansions of irregular conformal blocks corresponding to…

In this paper, extensions of nonunitary rational Virasoro vertex operator algebras corresponding to some exceptional modular invariants are constructed. The uniqueness of these extensions is also established.

In this paper, we introduce a notion of twisted restricted conformal blocks on totally ramified orbicurves and establish an isomorphism between the space of twisted restricted conformal blocks and the space of twisted conformal blocks. The…

Classical Virasoro conformal blocks are believed to be directly related to accessory parameters of Floquet type in the Heun equation and some of its confluent versions. We extend this relation to another class of accessory parameter…

Motivated by problems arising in the study of N=2 supersymmetric gauge theories we introduce and study irregular singularities in two-dimensional conformal field theory, here Liouville theory. Irregular singularities are associated to…

We perform a detailed study of a class of irregular correlators in Liouville Conformal Field Theory, of the related Virasoro conformal blocks with irregular singularities and of their connection formulae. Upon considering their…

We propose $q$-deformation of the Gamayun-Iorgov-Lisovyy formula for Painlev\'e $\tau$ function. Namely we propose formula for $\tau$ function for $q$-difference Painlev\'e equation corresponding to $A_7^{(1)}{}'$ surface (and $A_1^{(1)}$…

We study the relation of irregular conformal blocks with the Painlev\'e III$_3$ equation. The functional representation for the quasiclassical irregular block is shown to be consistent with the BPZ equations of conformal field theory and…

We propose a definition of irregular vertex operators in the H3+ WZW model. Our definition is compatible with the duality [1] between the H3+ WZW model and Liouville theory, and we provide the explicit map between correlation functions of…

In 2012 Gamayun, Iorgov, Lisovyy conjectured an explicit expression for the Painlev\'e VI $\tau$~function in terms of the Liouville conformal blocks with central charge $c=1$. We prove that proposed expression satisfies Painlev\'e VI…

We introduce the notion of irregular vertex (operator) algebras. The irregular versions of fundamental properties, such as Goddard uniqueness theorem, associativity and operator product expansions are formulated and proved. We also give…