A new cohomology class on the moduli space of stable curves

We define a collection of cohomology classes on the moduli space of curves. We prove that a generating function for the intersection numbers involving these new cohomology classes is a tau function of the KdV hierarchy, analogous to the Kontsevich-Witten theorem. The cohomology classes can be used to define a new type of Gromov-Witten invariant for any target variety