Related papers: The extended D-Toda hierarchy

Based on the large N duality relating topological string theory on Calabi-Yau 3-folds and Chern-Simons theory on 3-manifolds, M. Aganagic, A. Klemm, M. Marino and C. Vafa proposed the topological vertex (hep-th/0305132), an algorithm on…

Inspired by the forms of delay-Painleve equations, we consider some new differential-discrete systems of KdV, mKdV and Sine-Gordon - type related by simple one way Miura transformations to classical ones. Using Hirota bilinear formalism we…

The goal of the paper is to categorify Dijkgraaf-Witten theory, aiming at providing foundation for a direct construction of Dijkgraaf-Witten theory as an Extended Topological Quantum Field Theory. The main tool is cohomology with…

We show that there is a series of topological string theories whose integrable structure is described by the Toda lattice hierarchy. The monodromy group of the Frobenius manifold for the matter sector is an extension of the affine Weyl…

We propose a new bilinear Hirota equation for $\tau$-functions associated with the $E_8$ root lattice, that provides a "lens" generalisation of the $\tau$-functions for the elliptic discrete Painlev\'e equation. Our equations are…

We prove that the Frobenius structure constructed from the Gromov-Witten theory for an orbifold projective line with at most $r$ orbifold points is uniquely determined by the WDVV equations with certain natural initial conditions.

Let X be a smooth, complex Fano variety, and delta(X) its Lefschetz defect. It is known that if delta(X) is at least 4, then X is isomorphic to a product SxT, where dim T=dim X-2. In this paper we prove a structure theorem for the case…

We construct solutions of the 2-dimensional Toda-Hirota equation (2dTHE) expressed by the solutions of the system of so-called Euler-Poisson-Darboux equations (EPD) in N complex variables. The system of EPD arises naturally from the…

We examine the logarithmic Gromov-Witten cycles of a toric variety relative to its full toric boundary. The cycles are expressed as products of double ramification cycles and natural tautological classes in the logarithmic Chow ring of the…

Applying recent ideas of Carlet, Dubrovin and Zhang (to appear), who, following a suggestion of Eguchi and Yang (hep-th/9407134), study the logarithm of the Lax operator of the Toda lattice, we show that the equivariant Toda lattice…

We construct a tau cover of the generalized Drinfeld-Sokolov hierarchy associated to an arbitrary affine Kac-Moody algebra with gradations $\mathrm{s}\le\mathds{1}$ and derive its Virasoro symmetries. By imposing the Virasoro constraints we…

We derive a set of bilinear functional equations of Hirota type for the partition functions of the $sl(2)$ related integrable statistical models defined on a random lattice. These equations are obtained as deformations of the Hirota…

The auxiliary linear problems are presented for all discretization levels of the Hirota-Ohta system. The structure of these linear problems coincides essentially with the structure of Nonlinear Schr\"odinger hierarchy. The squared…

In this paper, we define Orlov-Schulman's operators $M_L$, $M_R$, and then use them to construct the additional symmetries of the bigraded Toda hierarchy (BTH). We further show that these additional symmetries form an interesting infinite…

A new class of integrable two-dimensional dilaton gravity theories, in which scalar matter fields satisfy the Toda equations, is proposed. The simplest case of the Toda system is considered in some detail, and on this example we outline how…

Orbifold generalizations of the ordinary and modified melting crystal models are introduced. They are labelled by a pair $a,b$ of positive integers, and geometrically related to $\mathbf{Z}_a\times\mathbf{Z}_b$ orbifolds of local…

Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau--Ginzburg orbifolds. Namely, for the pairs $(f,G)$, where $f$…

We present the Lax pair formalism for certain extension of the continuous limit of the classical Toda lattice hierarchy, provide a well defined notion of tau function for its solutions, and give an explicit formulation of the relationship…

Fordy and Xenitidis [J. Phys. A: Math. Theor. 50 (2017) 165205] recently proposed a large class of discrete integrable systems which include a number of novel integrable difference equations, from the perspective of $\mathbb{Z}_\mathcal{N}$…

We describe a formalism based on quantization of quadratic hamiltonians and symplectic actions of loop groups which provides a convenient home for most of known general results and conjectures about Gromov-Witten invariants of compact…