Intersection numbers from the antisymmetric Gaussian matrix model

TL;DR

This paper extends the antisymmetric Gaussian matrix model to orthogonal groups, deriving duality relations and calculating intersection numbers for non-orientable spin surfaces with marked points.

Contribution

It introduces a new duality relation for characteristic polynomial expectations and computes intersection numbers for non-orientable surfaces in this extended model.

Findings

Derived a duality relation for antisymmetric Gaussian matrix models.

Calculated intersection numbers for non-orientable spin surfaces.

Connected Fourier transforms of correlation functions to topological invariants.

Abstract

The matrix model of topological field theory for the moduli space of p-th spin curves is extended to the case of the Lie algebra of the orthogonal group. We derive a new duality relation for the expectation values of characteristic polynomials in the antisymmetric Gaussian matrix model with an external matrix source. The intersection numbers for non-orientable surfaces of spin curves with k marked points are obtained from the Fourier transform of the k-point correlation functions at the critical point where the gap is closing.