Black Holes and the SYM Phase Diagram

TL;DR

This work clarifies how the thermodynamic phase structure of M/string theory emerges from the combined Matrix theory and Maldacena dualities. By mapping finite-temperature SYM on a torus to its dual supergravity description, the authors construct a phase diagram for a DLCQ M-theory object in $4+1$ and $5+1$ dimensions, revealing phases such as matrix strings, matrix black holes, and $p$-brane configurations, and identifying a triple point where various transition lines converge. A key microscopic insight is the identification of a characteristic bump in the Matrix-string self-interaction potential at the thermal wavelength, which signals a transition to a black hole phase via longitudinal momentum transfer and clustering of partons, thereby providing a SYM-based mechanism for black hole formation. The results unify thermodynamic transitions through a common scaling and offer a framework to study non-perturbative M-theory thermodynamics and its holographic duals, including charged black holes and their clustering dynamics. These findings advance the understanding of how black-hole physics emerges from gauge theories and string theory in DLCQ settings, and they illuminate the role of finite-size effects and correspondence in non-perturbative regimes.

Abstract

Making combined use of the Matrix and Maldacena conjectures, the relation between various thermodynamic transitions in super Yang-Mills (SYM) and supergravity is clarified. The thermodynamic phase diagram of an object in DLCQ M-theory in four and five non-compact space dimensions is constructed; matrix strings, matrix black holes, and black $p$-branes are among the various phases. Critical manifolds are characterized by the principles of correspondence and longitudinal localization, and a triple point is identified. The microscopic dynamics of the Matrix string near two of the transitions is studied; we identify a signature of black hole formation from SYM physics.

Figures (7)

• Figure 1: The proposed thermodynamic phase diagram for the $p+1$d SYM on the torus, or the DLCQ IIA theory, obtained by tracking an object in Matrix theory. On the horizontal axis is the IIA string coupling, which is the aspect ratio of the SYM torus. The vertical axis is the density of states of the object.
• Figure 2: The string self-interaction potential as a function of relative separation $x$ along the string, for $p=4,5$.
• Figure 3: The entropy $S$ versus $g_s$ phase diagram showing the region of validity of the SYM description, and the boundary between the free and interacting phases, ignoring finite size effects. We assume $N,S \gg 1$, and $g_s< 1$, and fix $N$ for a given diagram.
• Figure 4: For the convenience of the reader, we reproduce Figure (\ref{['fig3']}): The proposed thermodynamic phase diagram for the $p+1$d SYM on the torus, i.e. the DLCQ IIA theory.
• Figure 5: $-K_\Delta$ as a function of the string separation parameter $x$; we see the change of scaling from $x^2$ to $x$.