On Self-dual Gravity Structures on Ground Ring Manifolds in Two-Dimensional String Theory

TL;DR

This paper explores the extension of geometric structures from Witten's ground ring in two-dimensional string theory, linking them to self-dual gravity and providing a twistor construction on the quantum ground ring manifold.

Contribution

It introduces a generalization of ground ring geometric structures incorporating self-dual gravity and develops a formal twistor construction for the quantum ground ring manifold.

Findings

Generalized geometric structures involve self-dual gravity.

A formal twistor construction on the quantum ground ring manifold is provided.

Connections between ground ring structures and self-dual gravity are established.

Abstract

We generalize the geometric structures generated by Witten's ground ring. It is shown that these generalized structures involve in a natural way some geometric constructions from Self-dual gravity [1,12]. The formal twistor construction on full quantum ground ring manifold is also given.