tt*-Geometry on the big phase space

TL;DR

This paper develops a Hermitian geometric framework for the big phase space in quantum cohomology, extending structures from the small phase space and showing tt*-geometry notions are preserved.

Contribution

It introduces a Hermitian geometry on the big phase space and demonstrates the preservation of tt*-geometry structures under lifting from the small phase space.

Findings

Hermitian structures are defined on the big phase space.

Notions of tt*-geometry are preserved during the lifting process.

The approach extends geometric structures from small to big phase space.

Abstract

The big phase space, the geometric setting for the study of quantum cohomology with gravitational descendents, is a complex manifold and consists of an infinite number of copies of the small phase space. The aim of this paper is to define a Hermitian geometry on the big phase space. Using the approach of Dijkgraaf and Witten, we lift various geometric structures of the small phase space to the big phase space. The main results of our paper state that various notions from tt*-geometry are preserved under such liftings.