相关论文: From Kontsevich-Witten to linear Hodge integrals v…

To a pair $(A,s)$ consisting of a smooth, cyclic $A_\infty$-algebra $A$ and a splitting $s$ of the Hodge filtration on its Hochschild homology Costello (2005) associates an invariant which conjecturally generalizes the total descendant…

In their recent inspiring paper Mironov and Morozov claim a surprisingly simple expansion formula for the Kontsevich-Witten tau-function in terms of the Schur Q-functions. Here we provide a similar conjecture for the Br\'ezin-Gross-Witten…

We prove the conjectural correspondence between logarithmic Gromov-Witten theory and logarithmic Donaldson/Pandharipande-Thomas theory for pairs $(Y|\partial Y)$ consisting of a toric threefold $Y$ and any torus invariant divisor $\partial…

We construct a quantum Hamiltonian operator for the Wess-Zumino-Witten (WZW) model in terms of the Casimir operator. This facilitates the discussion of the reduction of the WZW model to Toda field theory at the quantum level and provides a…

There are well-known constructions of integrable systems which are chains of infinitely many copies of the equations of the KP hierarchy ``glued'' together with some additional variables, e.g., the modified KP hierarchy. Another…

By considering spaces of directed Jacobi diagrams, we construct a diagrammatic version of the Etingof-Kazhdan quantization of complex semisimple Lie algebras. This diagrammatic quantization is used to provide a construction of a directed…

We study the 2-loop part of the rational Kontsevich integral of a knot in an integer homology sphere. We give a general formula which explains how the 2-loop part of the Kontsevich integral of a knot changes after surgery on a single…

Hurwitz numbers, which count certain covers of the projective line (or, equivalently, factorizations of permuations into transpositions), have been extensively studied for over a century. The Gromov-Witten potential F of a point, the…

We introduce an approach to expand gauge-invariant Wilson operators on lattice. This approach is based on non-abelian Stokes theorem and overcomes some shortage of some former methods. It is also suitable for expanding any Wilson operators…

In this paper, we obtain two Lichnerowicz type formulas for the Dirac-Witten operators. And we give the proof of Kastler-Kalau-Walze type theorems for the Dirac-Witten operators on 4-dimensional and 6- dimensional compact manifolds with…

Starting from the ELSV formula, we derive a number of new equations on the generating functions for Hodge integrals over the moduli space of complex curves. This gives a new simple and uniform treatment of certain known results on Hodge…

We consider a Lie algebra generalizing the Virasoro algebra to the case of two space variables. We study its coadjoint representation and calculate the corresponding Euler equations. In particular, we obtain a bi-Hamiltonian system that…

We show directly in the Lax operator approach how the Virasoro and W-constraints on the $\tau$-function arise in the $p$-reduced KP hierarchy or generalized KdV hierarchy. In partiacular, we consider the KdV and Boussinesq hierarchy to show…

We find the GKO coset construction of the dimension 4 Casimir operator that contains the quartic WZW currents contracted with completely symmetric SU(N) invariant tensors of ranks 4, 3, and 2. The requirements, that the operator product…

We study the Hodge numbers of Landau-Ginzburg models as defined by Katzarkov, Kontsevich and Pantev. First we show that these numbers can be computed using ordinary mixed Hodge theory, then we give a concrete recipe for computing these…

We prove a formula conjectured by the third author expressing certain Hodge integrals in terms of certain Chern-Simons link invariants. Such invariants also arise in the representation theory of Kac-Moody algebras.

The Kontsevich-Penner model, an Airy matrix model with a logarithmic potential, may be derived from a simple Gaussian two-matrix model through a duality. In this dual version the Fourier transforms of the n-point correlation functions can…

Several new formulas are developed that enable the evaluation of a family of definite integrals containing the product of two Whittaker W-functions. The integration is performed with respect to the second index, and the first index is…

Gromov-Witten (GW) theory produces Chow and cohomology classes on the moduli of curves, and there are several conjectures/speculations about their relation to the tautological ring. We develop new degeneration techniques to address these.…

Following and generalizing a construction by Kontsevich, we associate a zeta function to any matrix with entries in a ring of noncommutative Laurent polynomials with integer coefficients. We show that such a zeta function is an algebraic…