Probing black holes in non-perturbative gauge theory

TL;DR

Probing black holes in non-perturbative gauge theory investigates how semiclassical black-hole geometry and horizon thermodynamics emerge from the dual, strongly coupled quantum mechanics of $N$ D0-branes. The authors introduce a localized $0$-brane probe with a resolving time within a mean-field description of the black-hole background, and analyze the W-boson spectrum, probe potential, and entropy. They show that the effective probe potential matches supergravity outside the stretched horizon, while inside the horizon light W-bosons thermalize the probe, signaling breakdown of classical gravity and providing a gauge-theory derivation of the horizon–entropy relation $S_{ m bh} \\sim \\frac{N^2 T U_0^2}{g^2_{\\mathrm{YM}} N}$. These results support a microscopic understanding of horizon radius and entropy in the gauge theory context and suggest directions for including full gauge multiplets and dynamical probes.

Abstract

We use a 0-brane to probe a ten-dimensional near-extremal black hole with N units of 0-brane charge. We work directly in the dual strongly-coupled quantum mechanics, using mean-field methods to describe the black hole background non-perturbatively. We obtain the distribution of W boson masses, and find a clear separation between light and heavy degrees of freedom. To localize the probe we introduce a resolving time and integrate out the heavy modes. After a non-trivial change of coordinates, the effective potential for the probe agrees with supergravity expectations. We compute the entropy of the probe, and find that the stretched horizon of the black hole arises dynamically in the quantum mechanics, as thermal restoration of unbroken U(N+1) gauge symmetry. Our analysis of the quantum mechanics predicts a correct relation between the horizon radius and entropy of a black hole.

Figures (8)

• Figure 1: Bounds on $\omega_{\rm min}$ and $\omega_{\rm max}$ vs. $R$. Red: $\beta = 0.1$ (perturbative regime), blue: $\beta = 0.9$, green: $\beta = 3.8$. The short horizontal lines mark the corresponding temperatures.
• Figure 2: The propagator $\Delta^2(k)$, obtained by solving (\ref{['ContinueGap']}) at $\beta = 3.0$ and $R = 0.25$. The blue curve is the continued propagator. The green curve is reconstructed from the spectral density.
• Figure 3: The spectral density $\rho(\omega)$ at $\beta = 3.0$. Dark blue: $R = 1.0$, green: $R = 0.75$, red: $R = 0.5$, light blue: $R = 0.25$.
• Figure 4: The spectral density $\rho(\omega)$ at $\beta = 3.0$. Dark blue: $R = 4.0$, green: $R = 3.0$, red: $R = 2.0$, light blue: $R = 1.5$.
• Figure 5: The lightest $W$ mass as a function of $R$ at $\beta = 2.0$ (red), $\beta=3.0$ (green) and $\beta=4.0$ (blue).