Related papers: Genus expansion of open free energy in 2d topologi…
We study subleading corrections to the genus-zero free energy of the $\mathcal{N}=3$ Gaiotto-Tomasiello theory. In general, we obtain the endpoints and free energy as a set of parametric equations via contour integrals of the planar…
This note aims to provide an entr\'ee to two developments in two-dimensional topological gravity -- that is, intersection theory on the moduli space of Riemann surfaces -- that have not yet become well-known among physicists. A little over…
Recently R. Pandharipande, J. Solomon and R. Tessler initiated a study of the intersection theory on the moduli space of Riemann surfaces with boundary. They conjectured that the generating series of the intersection numbers is a specific…
We provide an integral formula for the free energy of the two-matrix model with polynomial potentials of arbitrary degree (or formal power series). This is known to coincide with the tau-function of the dispersionless two--dimensional Toda…
We sharpen the duality between open and closed topological string partition functions for topological gravity coupled to matter. The closed string partition function is a generalised Kontsevich matrix model in the large dimension limit. We…
A formula for the generating function of the Weil-Petersson volumes of moduli spaces of pointed curves that is identical to the genus expansion of the free energy in two dimensional gravity is obtained. The contribution of arbitrary genus…
In this paper we conjecture that the generating function of the intersection numbers on the moduli spaces of Riemann surfaces with boundary, constructed recently by R. Pandharipande, J. Solomon and R. Tessler and extended by A. Buryak, is a…
We apply the renormalized coupling constants and Virasoro constraints to derive the Itzykson-Zuber Ansatz on the form of the free energy in topological 2D gravity. We also treat the topological 1D gravity and the Hermitian one-matrix models…
We study the random geometry approach to the $T\bar{T}$ deformation of 2d conformal field theory developed by Cardy and discuss its realization in a gravity dual. In this representation, the gravity dual of the $T\bar{T}$ deformation…
We couple twisted non-compact N=(2,2) supersymmetric models to topological gravity in two dimensions. We propose expressions for the genus zero correlation functions based on a Kadomtsev-Petviashvili integrable hierarchy. Moreover, we prove…
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…
We find a volume form on moduli space of double punctured Riemann surfaces whose integral satisfies the Painlev\'e I recursion relations of the genus expansion of the specific heat of 2D gravity. This allows us to express the asymptotic…
We solve two-dimensional gravity on surfaces with boundary in terms of contact interactions and surface degenerations. The known solution of the bulk theory in terms of a contact algebra is generalized to include boundaries and an enlarged…
We present here the iteration procedure for the determination of free energy $\epsilon^{2}$-expansion using the theory of KdV - type equations. In our approach we use the conservation laws for KdV - type equations depending explicitly on…
We study multi-boundary correlators in 2d Witten-Kontsevich topological gravity. We present a proof of the loop equations obeyed by the correlators. While the loop equations were derived a long time ago, our proof is fully explicit in the…
The bi-Hamiltonian structure of the Benney hierarchy is revisited. We show that the compatibility condition of the Poisson brackets provides the genus zero free energy of a topological field theory coupled to 2d gravity. We calculate the…
We compute the complete topological expansion of the formal hermitian two-matrix model. For this, we refine the previously formulated diagrammatic rules for computing the 1/ N expansion of the nonmixed correlation functions and give a new…
We discuss the 1/N expansion of the free energy of N logarithmically interacting charges in the plane in an external field. For some particular values of the inverse temperature beta this system is equivalent to the eigenvalue version of…
We prove a formula for the genus one free energy $\mathcal{F}^{(1)}$ of the quartic Kontsevich model for arbitrary ramification by working out a boundary creation operator for blobbed topological recursion. We thus investigate the…
In our previous two papers, we constructed an $r$-spin theory in genus zero for Riemann surfaces with boundary and fully determined the corresponding intersection numbers, providing an analogue of Witten's $r$-spin conjecture in genus zero…