Related papers: Seiberg-Witten Theory and Extended Toda Hierarchy
We describe the magnetic phase of SU(N) $\mathcal{N}=2$ Super Yang-Mills theories in the self-dual Omega background in terms of a new class of multi-cut matrix models. These arise from a non-perturbative completion of topological strings in…
We present the first computation of the thermodynamic properties of the complex su(3) Toda theory. This is possible thanks to a new string hypothesis, which involves bound states that are non self-conjugate solutions of the Bethe equations.…
In a companion paper to this one, we proved that the Gromov--Witten theory of a Fano orbifold line of type $D$ is governed by a system of Hirota Bilinear Equations. The goal of this paper is to prove that every solution to the Hirota…
We propose a compact and explicit expression for the solutions of the complex Toda chains related to the classical series of simple Lie algebras g. The solutions are parametrized by a minimal set of scattering data for the corresponding Lax…
The main object of this paper is to produce a deformation of the KdV hierarchy of partial differential equations. We construct this deformation by taking a certain limit of the Toda hierarchy. This construction also provides a deformation…
A dual description of 3-dimensional topological Seiberg-Witten theory in terms of the Alexander invariant on manifolds obtained via surgery on a knot is proposed. The description directly follows from a low-energy analysis of the…
We consider the relation of the multi-component 2D Toda hierarchy with matrix orthogonal and biorthogonal polynomials. The multi-graded Hankel reduction of this hierarchy is considered and the corresponding generalized matrix orthogonal…
We introduce a new class of perturbations of the Seiberg-Witten equations. Our perturbations offer flexibility in the way the Seiberg-Witten invariants are constructed and also shed a new light to LeBrun's curvature inequalities.
We show that extremal correlators in all Lagrangian ${\cal N}=2$ superconformal field theories with a simple gauge group are governed by the same universal Toda system of equations, which dictates the structure of extremal correlators to…
Given a semisimple Frobenius manifold, we construct a class of integrable deformations of its hierarchy of topological type. We show that these integrable deformations have polynomial tau-structures, and conjecture that for the…
This is the sequel to the author's previous paper which gives an extension of Taubes' "SW=Gr" theorem to non-symplectic 4-manifolds. The main result of this paper asserts the following. Whenever the Seiberg-Witten invariants are defined…
We construct an explicit solution of the Seiberg-Witten map for a linear gauge field on the non-commutative plane. We observe that this solution as well as the solution for a constant curvature diverge when the non-commutativity parameter…
The role of integrable systems in string theory is discussed. We remind old examples of the correspondence between stringy partition functions or effective actions and integrable equations, based on effective application of the matrix model…
Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…
To any solution of a linear system of differential equations, we associate a kernel, correlators satisfying a set of loop equations, and in presence of isomonodromic parameters, a Tau function. We then study their semiclassical expansion…
We present a definition of the non-abelian generalisations of affine Toda theory related from the outset to vertex operator constructions of the corresponding Kac-Moody algebra $\gh$. Reuslts concerning conjugacy classes of the Weyl group…
We show the refinement of the prescription for the geometric transition in the refined topological string theory and, as its application, discuss a possibility to describe $qq$-characters from the string theory point of view. Though the…
We extend the generalized flux formulation of Double Field Theory to include all the first order bosonic contributions to the $\alpha '$ expansion of the heterotic string low energy effective theory. The generalized tangent space and…
We quantise the reduced theory obtained by substituting the soliton solutions of affine Toda theory into its symplectic form. The semi-classical S-matrix is found to involve the classical Euler dilogarithm.
We discuss the origin of the associativity (WDVV) equations in the context of quasiclassical or Whitham hierarchies. The associativity equations are shown to be encoded in the dispersionless limit of the Hirota equations for KP and Toda…