The combinatorial formula for open gravitational descendents

Abstract

In recent works, [20],[21], descendent integrals on the moduli space of Riemann surfaces with boundary were defined. It was conjectured in [20] that the generating function of these integrals satisfies the open KdV equations. In this paper we develop the notions of symmetric Strebel-Jenkins differentials and of Kasteleyn orientations for graphs embedded in open surfaces. In addition we write an explicit expression for the angular form of the sum of line bundles. Using these tools we prove a formula for the descendent integrals in terms of sums over weighted graphs. Based on this formula, the conjecture of [20] was proved in [5].

Improved the writing of some proofs and definitions, fixed some typos. To appear in G&T

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Cited by in corpus (14)

• Developments in Topological Gravity
• Matrix models and a proof of the open analog of Witten's conjecture
• Higher Airy structures and topological recursion for singular spectral curves
• Refined open intersection numbers and the Kontsevich-Penner matrix model
• Higher Airy structures, W algebras and topological recursion
• Open intersection numbers and free fields
• Combinatorial models for moduli spaces of open Riemann surfaces
• Open KdV hierarchy and minimal gravity on disk
• Extended $r$-spin theory in all genera and the discrete KdV hierarchy
• From minimal gravity to open intersection theory
• Open r-spin theory I: Foundations
• A construction of open descendant potentials in all genera
• Closed extended $r$-spin theory and the Gelfand-Dickey wave function
• On affine coordinates of the tau-function for open intersection numbers