The stringy nature of the 2d type-0A black hole

TL;DR

This paper studies the thermodynamics of the 2D type-0A black hole, resolving previous discrepancies with matrix model predictions by adjusting the cutoff, and explores its phase transition behavior near the Hagedorn temperature.

Contribution

It demonstrates how the cutoff choice affects free energy calculations and confirms the matrix model's accuracy in reproducing black hole thermodynamics, including entropy and phase transition insights.

Findings

Discrepancy in free energy is resolved with a fixed-distance cutoff.

Black hole entropy and mass match matrix model predictions.

Black hole exhibits Hagedorn growth indicating a phase transition.

Abstract

We investigate the thermodynamics of the RR charged two-dimensional type-0A black hole background at finite temperature, and compare with known 0A matrix model results. It has been claimed that there is a disagreement for the free energy between the spacetime and the dual matrix model. Here we find that this discrepancy is sensitive to how the cutoff is implemented on the spacetime side. In particular, the disagreement is resolved once we put the cutoff at a fixed distance away from the horizon, as opposed to a fixed position in space. Furthermore, the mass and the entropy of the black hole itself add up to an analytic contribution to the free energy, which is precisely reproduced by the 0A matrix model. We also use results from the 0A matrix model to predict the next to leading order contribution to the entropy of the black hole. Finally, we note that the black hole is characterized by a Hagedorn growth in its density of states below the Hagedorn temperature. This, together with other results, suggests there is a phase transition at this temperature.