Ground Ring Of Two Dimensional String Theory

TL;DR

This paper explores the ground ring structure in two-dimensional string theory, revealing its connection to symmetries like area and volume-preserving diffeomorphisms and relating string theory to matrix models.

Contribution

It characterizes the ground ring of operators in 2D string theory and links its symmetries to geometric transformations, enhancing understanding of the theory's structure and its relation to matrix models.

Findings

Identifies the ground ring as operators of spin (0,0).

Shows the symmetry groups are area and volume-preserving diffeomorphisms.

Connects the string theory symmetries to matrix model phase space.

Abstract

String theories with two dimensional space-time target spaces are characterized by the existence of a ``ground ring'' of operators of spin $(0,0)$. By understanding this ring, one can understand the symmetries of the theory and illuminate the relation of the critical string theory to matrix models. The symmetry groups that arise are, roughly, the area preserving diffeomorphisms of a two dimensional phase space that preserve the fermi surface (of the matrix model) and the volume preserving diffeomorphisms of a three dimensional cone. The three dimensions in question are the matrix eigenvalue, its canonical momentum, and the time of the matrix model.