Quantum Analysis of Jackiw and Teitelboim's Model for 1+1 D Gravity and Topological Gauge Theory

TL;DR

This paper performs a BRST quantization of the Jackiw-Teitelboim 1+1 D gravity model and its topological gauge theory equivalent, revealing their quantum equivalence and underlying superconformal structures.

Contribution

It provides a detailed BRST quantization of the JT gravity model and demonstrates its quantum equivalence to a topological gauge theory, uncovering superconformal symmetries.

Findings

Gravity model quantized as a free theory with nilpotent BRST charge

Existence of twisted N=2 superconformal algebras in both models

Quantum equivalence established between gravity and topological gauge theories

Abstract

We study the BRST quantization of the 1+1 dimensional gravity model proposed by Jackiw and Teitelboim and also the topological gauge model which is equivalent to the gravity model at least classically. The gravity model quantized in the light-cone gauge is found to be a free theory with a nilpotent BRST charge. We show also that there exist twisted N=2 superconformal algebras in the Jackiw-Teitelboim's model as well as in the topological gauge model. We discuss the quantum equivalence between the gravity theory and the topological gauge theory. It is shown that these theories are indeed equivalent to each other in the light-cone gauge.