Virasoro constraints for Hodge integrals

TL;DR

This paper investigates Virasoro constraints in Gromov-Witten theory for any target variety, proposing a conjecture, proving genus-zero and genus-one cases, and deriving new higher-genus vanishing identities.

Contribution

It introduces a Virasoro conjecture for Hodge integrals and proves key cases, advancing understanding of Gromov-Witten invariants across all target varieties.

Findings

Virasoro conjecture proposed for Hodge integrals in Gromov-Witten theory.

Virasoro constraints proven for genus-zero Hodge integrals.

Genus-1 $L_1^{ ext{E}}$ constraint established with one Hodge class insertion.

Abstract

The purpose of this paper is to study Virasoro constraints for Hodge integrals in Gromov-Witten theory of any target varieties. Results consist of the following: Firstly, we propose Virasoro conjecture for Hodge integrals in Gromov-Witten theory of any target varieties; Secondly, we prove Virasoro constraints for Hodge integrals in genus zero of any target varieties; Thirdly, we prove the genus-1 $L_1^{\mathbb{E}}$ constraint with one Hodge character class insertion for any target varieties; Lastly, we obtain certain new vanishing identities in higher genus for Gromov-Witten invariants of any target varieties.