On the sqrt{2} puzzle in AdS_2/CFT_1

TL;DR

This paper investigates the Hamiltonian structure of the Jackiw-Teitelboim model of 2D gravity, resolving a known sqrt{2} discrepancy in black hole entropy calculations by carefully analyzing boundary terms and asymptotic symmetries.

Contribution

It provides a detailed Hamiltonian analysis of the JT model, clarifying the central charge and resolving the sqrt{2} puzzle in black hole entropy.

Findings

No sqrt{2} discrepancy in entropy calculations

Corrected central charge associated with asymptotic symmetries

Boundary terms are crucial for accurate thermodynamic and statistical entropy matching

Abstract

In this letter we analyze the Hamiltonian formulation of the Jackiw-Teitelboim model of 2D gravity and calculate the central charge associated with the asymptotic symmetries, taking care of boundary terms. For black hole solutions, we show that there is no sqrt{2} discrepancy between the thermodynamical entropy and the statistical one obtained via Cardy's formula.