A construction of open descendant potentials in all genera

TL;DR

This paper develops a new framework for open Gromov-Witten invariants, constructing open descendant potentials across all genera using an extension of Givental's formalism, and verifies key recursion and string equations.

Contribution

It introduces an open analogue of Givental's action to construct open descendant and ancestor potentials for all genera, satisfying fundamental equations and recursion relations.

Findings

Constructs open total descendant potentials satisfying open WDVV equations.

Demonstrates that these potentials obey open topological recursion, string, and dilaton equations.

Computes the simplest nontrivial open correlator in genus 1.

Abstract

We 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.