Relations between the correlators of the topological sigma-model coupled to gravity
Abstract
We prove a new recursive relation between the correlators
<
τ
d
1
γ
1
...
τ
d
n
γ
n
>
g,β
, which together with known relations allows one to express all of them through the full system of Gromov-Witten invariants in the sense of Kontsevich-Manin and the intersection indices of tautological classes on
M
¯
g,n
, effectively calculable in view of earlier results due to Mumford, Kontsevich, Getzler, and Faber. This relation shows that a linear change of coordinates of the big phase space transforms the potential with gravitational descendants to another function defined completely in terms of the Gromov-Witten correspondence and the intersection theory on
V
n
×
M
¯
g,n
. We then extend the formalism of gravitational descendants from quantum cohomology to more general Frobenius manifolds and Cohomological Field Theories.