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Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics

Masanori Hanada, Yoshifumi Hyakutake, Jun Nishimura, Shingo Takeuchi

TL;DR

The power of the subleading term is shown to be nicely reproduced by the Monte Carlo data obtained nonperturbatively on the gauge theory side at finite but large effective (dimensionless) 't Hooft coupling constant.

Abstract

We perform a direct test of the gauge-gravity duality associated with the system of N D0-branes in type IIA superstring theory at finite temperature. Based on the fact that higher derivative corrections to the type IIA supergravity action start at the order of α'^3, we derive the internal energy in expansion around infinite 't Hooft coupling up to the subleading term with one unknown coefficient. The power of the subleading term is shown to be nicely reproduced by the Monte Carlo data obtained nonperturbatively on the gauge theory side at finite but large effective (dimensionless) 't Hooft coupling constant. This suggests, in particular, that the open strings attached to the D0-branes provide the microscopic origin of the black hole thermodynamics of the dual geometry including α' corrections. The coefficient of the subleading term extracted from the fit to the Monte Carlo data provides a prediction for the gravity side, which can be checked once the complete form of the O(α'^3) corrections to the supergravity action is obtained.

Higher derivative corrections to black hole thermodynamics from supersymmetric matrix quantum mechanics

TL;DR

The power of the subleading term is shown to be nicely reproduced by the Monte Carlo data obtained nonperturbatively on the gauge theory side at finite but large effective (dimensionless) 't Hooft coupling constant.

Abstract

We perform a direct test of the gauge-gravity duality associated with the system of N D0-branes in type IIA superstring theory at finite temperature. Based on the fact that higher derivative corrections to the type IIA supergravity action start at the order of α'^3, we derive the internal energy in expansion around infinite 't Hooft coupling up to the subleading term with one unknown coefficient. The power of the subleading term is shown to be nicely reproduced by the Monte Carlo data obtained nonperturbatively on the gauge theory side at finite but large effective (dimensionless) 't Hooft coupling constant. This suggests, in particular, that the open strings attached to the D0-branes provide the microscopic origin of the black hole thermodynamics of the dual geometry including α' corrections. The coefficient of the subleading term extracted from the fit to the Monte Carlo data provides a prediction for the gravity side, which can be checked once the complete form of the O(α'^3) corrections to the supergravity action is obtained.

Paper Structure

This paper contains 9 sections, 20 equations, 2 figures.

Table of Contents

  1. Introduction.---
  2. The dual black hole geometry.---
  3. Black hole thermodynamics.---
  4. Higher derivative corrections.---
  5. More on $\alpha '$ corrections.---
  6. The worldvolume theory.---
  7. Monte Carlo results.---
  8. Summary.---
  9. Acknowledgments.---

Figures (2)

  • Figure 1: The deviation of the internal energy $\frac{1}{N^2} E$ from the leading term $7.41 \, T^{\frac{14}{5}}$ is plotted against the temperature in the log-log scale for $\lambda=1$. The solid line represents a fit to a straight line with the slope 4.6 predicted from the $\alpha '$ corrections on the gravity side.
  • Figure 2: The internal energy $\frac{1}{N^2} E$ is plotted against $T$ for $\lambda=1$. The solid line represents the leading asymptotic behavior at small $T$ predicted by the gauge-gravity duality. The dashed line represents a fit to the behavior (\ref{['EvsTsub']}) including the subleading term with $C=5.58$.