A Construction of Open Descendant Potentials in All Genera

Abstract

AbstractWe present a construction of an open analogue of total descendant and total ancestor potentials via an “open version” of Givental’s action. Our construction gives a genus expansion for an arbitrary solution to the open WDVV equations satisfying a semisimplicity condition and admitting a unit. We show that the open total descendant potentials we define satisfy the open topological recursion relations in genus $0$ and $1$, the open string and open dilaton equations. We finish the paper with a computation of the simplest nontrivial open correlator in genus $1$ using our construction.