Dispersionless Integrable Hierarchy via Kodaira-Spencer Gravity

TL;DR

This paper demonstrates how dispersionless integrable hierarchies in 2d topological field theory originate from Kodaira-Spencer gravity, linking infinite symmetries to commuting Hamiltonians within a BV framework.

Contribution

It introduces a BV framework connecting Kodaira-Spencer gravity to dispersionless integrable hierarchies, revealing the role of abelian symmetries and current observables.

Findings

Infinite commuting Hamiltonians from Kodaira-Spencer gravity

BV framework clarifies B-model interpretation

Connection between symmetries and integrable hierarchies

Abstract

We explain how dispersionless integrable hierarchy in 2d topological field theory arises from the Kodaira-Spencer gravity (BCOV theory). The infinitely many commuting Hamiltonians are given by the current observables associated to the infinite abelian symmetries of the Kodaira-Spencer gravity. We describe a BV framework of effective field theories that leads to the B-model interpretation of dispersionless integrable hierarchy.