Spectrum of Two-Dimensional (Super)Gravity

TL;DR

This paper reviews the BRST analysis of 2D (super)gravity coupled with (super)conformal matter, detailing the spectrum, operator realization, and ground ring structure, with additional discussions on hermiticity and specific matter couplings.

Contribution

It provides a comprehensive review of the spectrum and operator structure in 2D supergravity coupled to conformal matter, including new insights into the ground ring and ghost number operators.

Findings

Spectrum and operator realization for nonzero ghost number states

Ground ring structure of super-Liouville with ${ ilde c}=1$ matter

Analysis of hermiticity and states for $c<1$ matter

Abstract

We review the BRST analysis of the system of a (super)conformal matter coupled to 2D (super)gravity. The spectrum and its operator realization are reported. In particular, the operators associated with the states of nonzero ghost number are given. We also discuss the ground ring structure of the super-Liouville coupled to ${\hat c}=1$ matter. In appendices, hermiticities, states for $c<1$ conformal matter coupled to gravity and the proof for the spectrum are discussed.