Gromov-Witten invariants of P1 coupled to a KdV tau function

Abstract

We consider the pull-back of a natural sequence of cohomology classes Θg,n∈H2(2g−2+n)(M‾g,n,Q) to the moduli space of stable maps M‾g,n(P1,d). These classes are related to the Brézin-Gross-Witten tau function of the KdV hierarchy via [Formula presented]. Insertions of the pull-backs of the classes Θg,n into the integrals defining Gromov-Witten invariants define new invariants which we show in the case of target P1 are given by a random matrix integral and satisfy the Toda equation.