c=1 String as a Topological Model

TL;DR

This paper demonstrates that the discrete states of the $c=1$ string can be understood as physical states within a topological sigma model, revealing a new geometric interpretation and algebraic structure.

Contribution

It introduces a new formulation of the $c=1$ string states as a topological sigma model, connecting discrete states to a graded ring structure and ground ring coordinate.

Findings

Discrete states form a graded ring including the ground ring

Ground ring generator x acts as a sigma model coordinate

Reformulation of BRST charge and energy-momentum tensor in topological terms

Abstract

The discrete states in the $c=1$ string are shown to be the physical states of a certain topological sigma model. We define a set of new fields directly from $c=1$ variables, in terms of which the BRST charge and energy-momentum tensor are rewritten as those of the topological sigma model. Remarkably, ground ring generator $x$ turns out to be a coordinate of the sigma model. All of the discrete states realize a graded ring which contains ground ring as a subset.