On the Twisted $N=2$ Superconformal Structure in $2d$ Gravity Coupled to Matter

TL;DR

This paper demonstrates that 2D gravity coupled to matter exhibits an infinite twisted N=2 superconformal symmetry, with different central charges in different gauges, and relates physical states across gauges via field redefinition.

Contribution

It reveals the presence of twisted N=2 superconformal symmetry in 2D gravity-matter systems and connects gauge descriptions through field redefinition.

Findings

Infinite twisted N=2 superconformal symmetry in 2D gravity with matter.

Different central charges in conformal and light cone gauges.

Physical states related by field redefinition across gauges.

Abstract

It is shown that the two dimensional gravity, described either in the conformal gauge (the Liouville theory) or in the light cone gauge, when coupled to matter possesses an infinite number of twisted $N=2$ superconformal symmetries. The central charges of the $N=2$ algebra for the two gauge choices are in general different. Further, it is argued that the physical states in the light cone gauge theory can be obtained from the Liouville theory by a field redefinition.