A proposal on the topological sector of 2d string

TL;DR

This paper studies the topological sector of 2D string theory as a spacetime gauge theory with a $w_$ algebra, explaining discrete states and proposing a deformation to include higher-order corrections.

Contribution

It introduces a gauge theory framework for the topological sector of 2D string theory using a $w_$ algebra and connects it to the emergence of discrete states and $$ corrections.

Findings

The topological sector can be described by a $w_$ algebra-based gauge theory.

Discrete states naturally emerge in this formulation.

Higher order $$ corrections are conjectured to deform the $w_$ algebra.

Abstract

The field content of the two dimensional string theory consists of the dynamical tachyon field and some nonpropagating fields which consist in the topological sector of this theory. We propose in this paper to study this topological sector as a spacetime gauge theory with a simple centrally extended $w_\infty$ algebra. This $w_\infty$ algebra appears in both the world sheet BRST analysis and the matrix model approach. Since the two dimensional centrally extended Poincar\'e algebra is naturally embedded in the centrally extended $w_\infty$ algebra, the low energy action for the metric and dilaton appears naturally when the model is truncated at this level. We give a plausible explanation of emergence of discrete states in this formulation. This theory is again the effective theory at zero slope limit. To include higher order $\alpha'$ corrections, we speculate that the whole theory is a gauge theory of a deformed $w_\infty$ algebra, and the deformation parameter is just $\alpha'$.