Action, Hamiltonian and CFT for 2D black holes

TL;DR

This paper analyzes boundary terms in the Hamiltonian for 2D AdS black holes, reconciling Euclidean methods with CFT predictions and clarifying the role of boundary conditions in gravitational theories.

Contribution

It demonstrates the precise agreement between Euclidean approaches and Cardy's formula in 2D black holes by properly accounting for boundary conditions and boundary terms in the Hamiltonian.

Findings

Boundary terms are crucial for Hamiltonian analysis in 2D black holes.

No discrepancy factor arises when boundary conditions are correctly applied.

Agreement between Euclidean methods and CFT is established under certain spectrum assumptions.

Abstract

The boundary terms in the Hamiltonian, in the presence of horizons, are carefully analyzed in a simple 2D theory admitting AdS black holes. The agreement between the euclidean approach and Cardy's formula is obtained modulo certain assumptions on the spectrum of the Virasoro's algebra. There is no discrepancy factor "square root of 2" once the appropriate boundary conditions are properly recognized. The peculiar features of gravity, that the on-shell Hamiltonian is determined by boundary terms, is the reason of the mentioned agreement.