Extra States and Symmetries in D<2 Closed String Theory

TL;DR

This paper explores the rich structure of closed string states in minimal conformal field theories coupled to 2D quantum gravity, revealing new symmetries and cohomology at various ghost numbers.

Contribution

It uncovers a large semi-relative BRST cohomology at non-positive ghost numbers and proposes an extended algebra from symmetry currents at negative ghost numbers.

Findings

Identification of (p-1)(p'-1) dimensional cohomology at each non-positive ghost number.

Relation of these states to currents and symmetry charges of exotic ghost number.

Conjecture on the extended algebra from negative ghost number currents.

Abstract

We show that there is (p-1)(p'-1) dimensional semi-relative BRST cohomology at each non-positive ghost number in the (p,p') minimal conformal field theory coupled to two dimensional quantum gravity. These closed string states are related to currents and symmetry charges of `exotic' ghost number. We investigate the symmetry structure generated by the most conventional currents (those of vanishing total ghost number), and make a conjecture about the extended algebra which results from incorporating the currents at negative ghost number.