Getzler relation and Virasoro conjecture for genus one

TL;DR

This paper derives universal equations for genus one Gromov-Witten invariants using Getzler's relation and offers evidence supporting the genus-1 Virasoro conjecture.

Contribution

It introduces explicit universal equations for genus one invariants and applies them to support the Virasoro conjecture at genus one.

Findings

Derived explicit equations for genus one invariants.

Provided evidence for the genus-1 Virasoro conjecture.

Connected Getzler's relation to quantum powers of Euler vector field.

Abstract

We derive explicit universal equations for primary Gromov-Witten invariants by applying Getzler's genus one relation to quantum powers of Euler vector field. As an application, we provide some evidences for the genus-1 Virasoro conjecture.