Related papers: Virasoro constraints for Kontsevich-Hurwitz partit…
In this short note we construct a simple cut-and-join operator representation for Kontsevich-Witten tau-function that is the partition function of the two-dimensional topological gravity. Our derivation is based on the Virasoro constraints.…
Using the thermodynamics formalism, we introduce a notion of intersection for projective Anosov representations, show analyticity results for the intersection and the entropy, and rigidity results for the intersection. We use the…
We summarize the recent results about complete solvability of Hermitian and rectangular complex matrix models. Partition functions have very simple character expansions with coefficients made from dimensions of representation of the linear…
Virasoro constraint is the operator algebra version of one-loop equation for a Hermitian one-matrix model, and it plays an important role in solving the model. We construct the realization of the Virasoro constraint from the Conformal Field…
In this paper, we show that the generating function for linear Hodge integrals over moduli spaces of stable maps to a nonsingular projective variety $X$ can be connected to the generating function for Gromov-Witten invariants of $X$ by a…
We study the root of unity limit of $(\textbf{q}, \textbf{t})$-deformed Virasoro matrix models, for which we call the resulting model Uglov matrix model. We derive the associated Virasoro constraints on the partition function and find…
We attempt to reconstruct the irreducible unitary representations of the Banach Lie group $U_0(\H)$ of all unitary operators $U$ on a separable Hilbert space $\H$ for which $U-{\mathbb I}$ is compact, originally found by Kirillov and…
Following our reformulation of sheaf-theoretic Virasoro constraints with applications to curves and surfaces joint with Lim-Moreira, I describe in the present work the quiver analog. After phrasing a universal approach to Virasoro…
Following ideas from the Abstract Interpolation Problem of Katsnelson et al. (Operators in spaces of functions and problems in function theory, vol 146, pp 83-69, Naukova Dumka, Keiv, 1987) for Schur class functions, we study a general…
We introduce Virasoro operators for any Landau-Ginzburg pair (W, G) where W is a non-degenerate quasi-homogeneous polynomial and G is a certain group of diagonal symmetries. We propose a conjecture that the total ancestor potential of the…
We continue our investigation of the Kontsevich--Penner model, which describes intersection theory on moduli spaces both for open and closed curves. In particular, we show how Buryak's residue formula, which connects two generating…
An indefinite variant of the abstract interpolation problem is considered. Associated to this problem is a model Pontryagin space isometric operator V. All the solutions of the problem are shown to be in a one-to-one correspondence with a…
We formulate Virasoro constraints for the generating functions of the intersection numbers on Hassett's moduli of weighted pointed curves and show that they are governed by the KdV integrable hierarchy.
The review is devoted to the integrable properties of the Generalized Kontsevich Model which is supposed to be an universal matrix model to describe the conformal field theories with $c<1$. It is shown that the deformations of the…
We consider the deformations of ``monomial solutions'' to Generalized Kontsevich Model \cite{KMMMZ91a,KMMMZ91b} and establish the relation between the flows generated by these deformations with those of $N=2$ Landau-Ginzburg topological…
We study the Virasoro constraints for moduli spaces of representations of quiver with relations by Joyce's vertex algebras. Using the framed Virasoro constraints, we construct a representation of half of the Virasoro algebra on the…
We prove a general mirror duality theorem for a subalgebra $U$ of a simple conformal vertex algebra $A$ and its commutant $V=\mathrm{Com}_A(U)$. Specifically, we assume that $A\cong\bigoplus_{i\in I} U_i\otimes V_i$ as a $U\otimes…
The Virasoro constraints play the important role in the study of matrix models and in understanding of the relation between matrix models and CFTs. Recently the localization calculations in supersymmetric gauge theories produced new…
Based on the Adler-Shiota-van Moerbeke (ASvM) formula, the Virasoro constraints and W-constraints for the p-reduced q-deformed Kadomtsev-Petviashvili (q-KP) hierarchy are established.
We study cosmological vector and tensor perturbations in Horava-Lifshitz gravity, adopting the most general Sotiriou-Visser-Weinfurtner generalization without the detailed balance but with projectability condition. After deriving the…