Non-existence of a dilaton gravity action for the exact string black hole

TL;DR

This paper proves that no local two-dimensional dilaton gravity theory without higher derivatives can exactly describe the string black hole solution, emphasizing the importance of dilaton-shift invariance.

Contribution

It demonstrates the non-existence of a local dilaton gravity action for the exact string black hole and classifies all dilaton-shift invariant models.

Findings

No local dilaton gravity action describes the exact string black hole.

Two dilaton-shift invariant models are explicitly constructed and analyzed.

The concept of dilaton-shift invariance is crucial for understanding these theories.

Abstract

We prove that no local diffeomorphism invariant two-dimensional theory of the metric and the dilaton without higher derivatives can describe the exact string black hole solution found a decade ago by Dijkgraaf, Verlinde and Verlinde. One of the key points in this proof is the concept of dilaton-shift invariance. We present and solve (classically) all dilaton-shift invariant theories of two-dimensional dilaton gravity. Two such models, resembling the exact string black hole and generalizing the CGHS model, are discussed explicitly.