Chiral gravity in two dimensions

TL;DR

This paper demonstrates the consistent coupling of chiral matter to two-dimensional frame gravity, quantizes the theory, and constructs a non-critical heterotic string with specific spectral properties, revealing no $c=1$ barrier.

Contribution

It introduces a consistent framework for chiral matter coupled to 2D gravity and constructs a novel non-critical heterotic string with a detailed spectrum.

Findings

SL(2,C) invariance leads to new super-selection rules

No $c=1$ barrier in chiral non-critical strings

Constructed heterotic string with 744 states in the adjoint of $(E_8)^3$

Abstract

It is shown that conformal matter with $c_{\ssc L}\not=c_{\ssc R}$ can be consistently coupled to two-dimensional `frame' gravity. The theory is quantized, following David, and Distler and Kawai, using the derivation of their {\it ansatz} due to Mavromatos and Miramontes, and D'Hoker and Kurzepa. New super-selection rules are found by requiring SL(2,{\bf C}) invariance of correlation functions on the plane. There is no analogue of the $c=1$ barrier found in non-chiral non-critical strings. A non-critical heterotic string is constructed---it has 744 states in its spectrum, transforming in the adjoint representation of $(E_8)^3.$ Correlation functions are calculated in this example.