Jackiw-Teitelboim Gravity as a Noncritical String

TL;DR

This paper explores Jackiw-Teitelboim gravity coupled with Liouville and matter fields, interpreting it as a non-critical string theory, and analytically computes the four-point correlation function revealing key properties like monodromy invariance and crossing symmetry.

Contribution

It introduces a novel interpretation of JT gravity as a non-critical string theory and provides an explicit analytical derivation of the four-point correlation function in this setup.

Findings

Analytical expression for the four-point correlation function.

Demonstration of properties like monodromy invariance and crossing symmetry.

Insight into the neutralization of the Liouville mode due to constant curvature constraint.

Abstract

Jackiw Teitelboim (JT) gravity has proven to be an excellent tool for investigating aspects of quantum gravity and black hole physics. In recent years, the study of JT gravity and its deformations has helped us learn about the different contributions of geometries in the gravitational path integral, the quantum gravity Hilbert space, the space-time factorization problem, the role of averaging in holography, the black hole information paradox, and the matrix models. All this motivates the exploration of the JT gravity in different setups, with and without matter. Here, we consider JT gravity conformally coupled to Liouville field theory and matter fields. This model admits to be interpreted as a non-critical string theory on a linear dilaton background with a tachyonic Liouville potential along a null direction. The constant curvature constraint of JT gravity results in a neutralization of the Liouville mode, which makes it possible to compute the four-point correlation function of the theory analytically. Here we give the explicit derivation of the four-point function and briefly comment on its properties, such as monodromy invariance, crossing symmetry, factorization, and limits.