相关论文: A Formula for Connected Bosonic \(n\)-Point Functi…

Orthogonal and symplectic matrix integrals are investigated. It is shown that the matrix integrals can be considered as a $\tau$-function of the coupled KP hierarchy, whose solution can be expressed in terms of pfaffians.

Give a convenient new approach to obtain the algebraic constraints on tau functions of p-reduced KP with the constraints of string equation. The classical results about algebraic constraints on associated tau function are included.

We first review the properties of the conventional $\tau$-functions of the KP and Toda-lattice hierarchies. A straightforward generalization is then discussed. It corresponds to passing from differential to finite-difference equations; it…

We study four dimensional supersymmetric gauge theory in the presence of surface and point-like defects (blowups) and propose an identity relating partition functions at different values of $\Omega$-deformation parameters…

We give a new formula for the energy functionals E_k defined by Chen-Tian, and discuss the relations between these functionals. We also apply our formula to give a new proof of the fact that the holomorphic invariants corresponding to the…

This article is concerned with obtaining the standard tau function descriptions of integrable equations (in particular, here the KdV and Ernst equations are considered) from the geometry of their twistor correspondences. In particular, we…

We show that the generating series of some Hodge integrals involving one or two partitions are tau-functions of the KP hierarchy or the 2-Toda hierarchy respectively. We also formulate a conjecture on the connection between relative…

Matrix hierarchies are: multi-component KP, general Zakharov-Shabat (ZS) and its special cases, e.g., AKNS. The ZS comprises all integrable systems having a form of zero-curvature equations with rational dependence of matrices on a spectral…

Analytic-bilinear approach for construction and study of integrable hierarchies, in particular, the KP hierarchy is discussed. It is based on the generalized Hirota identity. This approach allows to represent generalized hierarchies of…

We prove the dispersionless Hirota equations for the dispersionless Toda, dispersionless coupled modified KP and dispersionless KP hierarchies using an idea from classical complex analysis. We also prove that the Hirota equations…

We propose a new method for the computation of quantum three-point functions for operators in su(2) sectors of N=4 super Yang-Mills theory. The method is based on the existence of a unitary transformation relating inhomogeneous and…

We review various aspects of integrable hierarchies appearing in N=2 supersymmetric gauge theories. In particular, we show that the blowup function in Donaldson-Witten theory, up to a redefinition of the fast times, is a tau function for a…

We present a unified description of birational representation of Weyl groups associated with T-shaped Dynkin diagrams, by using a particular configuration of points in the projective plane. A geometric formulation of tau-functions is given…

Exact non-perturbative partition functions of coupling constants and external fields exhibit huge hidden symmetry, reflecting the possibility to change integration variables in the functional integral. In many cases this implies also some…

A characterization of the Kadomtsev-Petviashvili hierarchy of type C (CKP) in terms of the KP tau-function is given. Namely, we prove that the CKP hierarchy can be identified with the restriction of odd times flows of the KP hierarchy on…

We establish an explicit formula for the n-point correlation functions in the sense of Bloch-Okounkov for the irreducible representations of $\hat{gl}_\infty$ and $W_{1+\infty}$ of arbitrary positive integral levels.

In this paper, we construct a new integrable equation which is a generalization of $q$-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of the generalized $q$-Toda…

We investigate correlation functions in a periodic box-ball system. For the second and the third nearest neighbor correlation functions, we give explicit formulae obtained by combinatorial methods. A recursion formula for a specific…

We introduce hypergeometric functions related to projective Schur functions $Q_{\lambda}$ and describe their properties. Linear equations, integral representations and Pfaffian representations are obtained. These hypergeometric functions…

We introduce certain B\"acklund transformations for rational solutions of the Painlev\'e VI equation. These transformations act ona family of Painlev\'e VI tau functions. They are obtained from reducing the Hirota bilinear equations that…