The Excess Intersection Formula and Gravitational Correlators

Abstract

The genus zero Gromov-Witten invariants of a homogeneous variety X generally solve an enumerative problem of rational curves with conditions of incidence to cycles in general position in X. In this paper we compute the same Gromov-Witten invariants with cycles in special position. The invariants can then be reinterpreted, using the excess intersection formula, as the sum of a contribution from a component of excess dimension and a contribution of the expected dimension. The excess contribution is identified with a sum of gravitational correlators, which can be computed using well-known recursive equations from the Gromov-Witten invariant. As a result, the contribution of the right dimension, which solves the enumerative problem requiring rational curves in X to have a node on a given cycle, can be computed in terms of Gromov-Witten invariants and gravitational correlators.