The Gregory-Laflamme instability for the D2-D0 bound state

TL;DR

The paper analyzes the Gregory-Laflamme instability of the non-extremal D2-D0 bound state, showing that the instability threshold aligns with local thermodynamic stability via the correlated stability conjecture (CSC). It derives the thermodynamic boundary det $H=0$, equivalent to $\mu_0^2 + 4\mu_2^2 = 1$, and corroborates this via a numerical linearized perturbation analysis around the supergravity background. In the NCFT limit, the critical temperature scales as $\sqrt{\vartheta} T_c = \dfrac{5\cdot 3^{1/10}}{2^{17/10}\pi^{9/10}} \dfrac{1}{(g_s N_2)^{1/5}} (\cot\theta)^{3/10} [1 - \dfrac{8}{5}\cot^2\theta + \cdots]$, which vanishes as $\alpha'/\vartheta \to 0$, suggesting instability may occur only at very long wavelengths or be absent on fixed-size manifolds. The authors explicitly construct stationary, inhomogeneous perturbations via a two-dimensional reduction and solve the linearized equations numerically, finding results in strong agreement with CSC predictions. Together, these findings illuminate how GL instabilities in brane bound states interplay with NCFT decoupling and offer a framework for analyzing stability across related bound-state configurations.

Abstract

The D2-D0 bound state exhibits a Gregory-Laflamme instability when it is sufficiently non-extremal. If there are no D0-branes, the requisite non-extremality is finite. When most of the extremal mass comes from D0-branes, the requisite non-extremality is very small. The location of the threshhold for the instability is determined using a local thermodynamic analysis which is then checked against a numerical analysis of the linearized equations of motion. The thermodynamic analysis reveals an instability of non-commutative field theory at finite temperature, which may occur only at very long wavelengths as the decoupling limit is approached.

Figures (3)

• Figure 1: The thick curve indicates the boundary of stability. The shaded region is the unstable region. The thin curves show constant $M$ for fixed $Q = \sqrt{Q_2^2+Q_0^2}$: the outermost of these curves is at $M=Q$, the next is at $M = 1.15 Q$, and so on with even spacing continuing to $M = 2.5 Q$. The vertical axis and horizontal axis show, respectively, the fraction of the mass that comes from D0-branes and D2-branes; the rest of the mass is non-extremality.
• Figure 2: Left: the minimum of $\tilde{T}$ for various values of $\alpha$ and $\theta$. In the final column, "False" means that a normalizable solution should exist according to the CSC, and "True" means that it shouldn't. Right: the position of these $16$ points in the $Q_2/M$, $Q_0/M$ plane. A red dot indicates that a normalizable mode was found, and a green dot indicates that it wasn't.
• Figure 3: The normalizable mode for the point labeled 12 in figure \ref{['figB']}.