相关论文: On determinant representation and integrability of…

We propose a systematic approach to calculating $n$-point one-loop parametric conformal integrals in $D$ dimensions which we call the reconstruction procedure. It relies on decomposing a conformal integral over basis functions which are…

The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Discrete 1-matrix, 2-matrix, ``conformal'' (multicomponent) and Kontsevich models are considered in some detail, together with the…

This is an introductory course on nonlinear integrable partial differential and differential-difference equ\-a\-ti\-ons based on lectures given for students of Moscow Institute of Physics and Technology and Higher School of Economics. The…

For every multivariable polynomial $p$, with $p(0)=1$, we construct a determinantal representation $$p=\det (I - K Z),$$ where $Z$ is a diagonal matrix with coordinate variables on the diagonal and $K$ is a complex square matrix. Such a…

We study the quantization of Hitchin systems in terms of beta-deformations of generalized matrix models related to conformal blocks of Liouville theory on punctured Riemann surfaces. We show that in a suitable limit, corresponding to the…

Gamayun, Iorgov and Lisovyy in 2012 proposed that tau function of the Painlev\'e equation is equal to the series of $c=1$ Virasoro conformal blocks. We study similar series of $c=-2$ conformal blocks and relate it to Painlev\'e theory. The…

We first review some invariant theoretic results about the finite subgroups of SU(2) in a quick algebraic way by using the McKay correspondence and quantum affine Cartan matrices. By the way it turns out that some parameters (a,b,h;p,q,r)…

Generalized convolution symmetries of integrable hierarchies of KP and 2KP-Toda type multiply the Fourier coefficients of the elements of the Hilbert space $\HH= L^2(S^1)$ by a specified sequence of constants. This induces a corresponding…

A powerful approach to the celebrated Wess-Zumino-Witten (WZW) model is provided by its free-field realization. However, explicit calculations of conformal blocks are not described in the literature in full detail. We begin this study with…

We uncover a combinatorial structure governing the differential equations satisfied by wavefunction coefficients of scalar fields with generic masses in de Sitter space. Using an integral representation of the massive mode functions, we…

We characterize a holomorphic positive definite function $f$ defined on a horizontal strip of the complex plane as the Fourier-Laplace transform of a unique exponentially finite measure on $\mathbb{R}$. The classical theorems of Bochner on…

The path integral description of the Wess-Zumino-Witten $\to$ Liouville reduction is formulated in a manner that exhibits the conformal invariance explicitly at each stage of the reduction process. The description requires a conformally…

We construct the general solution of a class of Fuchsian systems of rank $N$ as well as the associated isomonodromic tau functions in terms of semi-degenerate conformal blocks of $W_N$-algebra with central charge $c=N-1$. The simplest…

We extend the proof from arXiv:1012.3137, which interprets the AGT relation as the Hubbard-Stratonovich duality relation to the case of 5d gauge theories. This involves an additional q-deformation. Not surprisingly, the extension turns out…

I establish the relation of the non-commutative BV-formalism with super-invariant matrix integration. In particular, the non-commutative BV-equation, defining the quantum A-infinity-algebras, introduced in "Modular operads and…

The phase space path integral Wess-Zumino-Witten $\to$ Toda reductions are formulated in a manifestly conformally invariant way. For this purpose, the method of Batalin, Fradkin, and Vilkovisky, adapted to conformal field theories, with…

A system of Bethe-Ansatz type equations, which specify a unique array of Young tableau responsible for the leading contribution to the Nekrasov partition function in the $\epsilon_2\rightarrow 0$ limit is derived. It is shown that the…

All unitary Rational Conformal Field Theories (RCFT) are conjectured to be related to unitary coset Conformal Field Theories, i.e., gauged Wess-Zumino-Witten (WZW) models with compact gauge groups. In this paper we use subfactor theory and…

A Fourier-type integral representation for Bessel's function of the first kind and complex order is obtained by using the Gegenbuaer extension of Poisson's integral representation for the Bessel function along with a trigonometric integral…

The Brezin-Gross-Witten (BGW) model is one of the basic examples in the class of non-eigenvalue unitary matrix models. The generalized BGW tau-function $\tau_N$ was constructed from a one parametric deformation of the original BGW model…