Topological Cigar and the c=1 String : Open and Closed

TL;DR

This paper explores the correspondence between c=1 string theory at the self-dual radius and the topologically twisted cigar model, establishing mappings of D-branes, open string spectra, and algebraic structures.

Contribution

It clarifies the map between two theories, relating D-branes, spectra, and algebraic structures, including a novel representation of an extended N=2 algebra on the worldsheet.

Findings

ZZ and FZZT branes correspond to localized and extended branes in the cigar model.

Open string spectra and two-point correlators are equivalent in both theories.

An extended N=2 algebra with higher spin currents is constructed on the worldsheet.

Abstract

We clarify some aspects of the map between the c=1 string theory at self-dual radius and the topologically twisted cigar at level one. We map the ZZ and FZZT D-branes in the c=1 string theory at self dual radius to the localized and extended branes in the topological theory on the cigar. We show that the open string spectrum on the branes in the two theories are in correspondence with each other, and their two point correlators are equal. We also find a representation of an extended N=2 algebra on the worldsheet which incorporates higher spin currents in terms of asymptotic variables on the cigar.