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# Communications in Number Theory and Physics

## Volume 10 (2016)

### Number 4

### Topological recursion for open intersection numbers

Pages: 833 – 857

DOI: http://dx.doi.org/10.4310/CNTP.2016.v10.n4.a5

#### Author

#### Abstract

We present a topological recursion formula for calculating the intersection numbers defined on the moduli space of open Riemann surfaces. The spectral curve is $x = \frac{1}{2} y^2$, the same as the spectral curve used to calculate intersection numbers for closed Riemann surfaces, but the formula itself is a variation of the usual Eynard–Orantin recursion. It looks like the recursion formula used for spectral curves of degree $3$, and also includes features present in $\beta$-deformed models. The recursion formula suggests a conjectural refinement to the generating function that allows for distinguishing intersection numbers on moduli spaces with different numbers of boundary components.