The complex Liouville string: the gravitational path integral

TL;DR

This paper rigorously defines sine dilaton gravity via the complex Liouville string, revealing new saddle points in the gravitational path integral and exploring transitions between AdS and dS vacua.

Contribution

It provides a rigorous worldsheet definition of sine dilaton gravity and uncovers novel saddle points contributing to its gravitational path integral.

Findings

Identification of new saddle points in the path integral

Transitions between AdS$_2$ and dS$_2$ vacua

Analysis of sphere and disk partition functions

Abstract

We give a rigorous definition of sine dilaton gravity in terms of the worldsheet theory of the complex Liouville string arXiv:2409.17246. The latter has a known exact solution that we leverage to explore the gravitational path integral of sine dilaton gravity - a quantum deformation of dS JT gravity that admits both AdS$_2$ and dS$_2$ vacua. We uncover that the gravitational path integral receives contributions from new saddles describing transitions between vacua in a third-quantized picture. We also discuss the sphere and disk partition function in this context and contrast our findings with other recent work on this theory.