Semi-classical dilaton gravity and the very blunt defect expansion

TL;DR

This paper investigates semi-classical dilaton gravity with general potentials, revealing a non-perturbative ambiguity in the canonical quantization approach and proposing new saddle points that influence the density of states and classical geometries.

Contribution

It uncovers a non-perturbative ambiguity in geodesic gauge quantization and introduces new saddle points affecting the understanding of dilaton gravity's density of states.

Findings

Identification of a non-perturbative ambiguity at the disk level in geodesic gauge.

Proposal of new saddles contributing to the density of states in dilaton gravity.

Derivation of classical geometries from a dense gas of blunt defects in the semi-classical limit.

Abstract

We explore dilaton gravity with general dilaton potentials in the semi-classical limit viewed both as a gas of blunt defects and also as a semi-classical theory in its own right. We compare the exact defect gas picture with that obtained by naively canonically quantizing the theory in geodesic gauge. We find a subtlety in the canonical approach due to a non-perturbative ambiguity in geodesic gauge. Unlike in JT gravity, this ambiguity arises already at the disk level. This leads to a distinct mechanism from that in JT gravity by which the semi-classical approximation breaks down at low temperatures. Along the way, we propose that new, previously un-studied saddles contribute to the density of states of dilaton gravity. This in particular leads to a re-interpretation of the disk-level density of states in JT gravity in terms of two saddles with fixed energy boundary conditions: the disk, which caps off on the outer horizon, and another, sub-leading complex saddle which caps off on the inner horizon. When the theory is studied using a defect expansion, we show how the smooth classical geometries of dilaton gravity arise from a dense gas of very blunt defects in the $G_N \to 0$ limit. The classical saddle points arise from a balance between the attractive force on the defects toward negative dilaton and a statistical pressure from the entropy of the configuration. We end with speculations on the nature of the space-like singularity present inside black holes described by certain dilaton potentials.