c=1 String as a Topological Model

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.

23 pages + 3 figures in PostScript, LaTeX, UT-Komaba/93-7. Description of the $c=1$ physical spectrum in terms of topological model is improved. Some references and new figures added. (figures are available upon request.)