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Black Holes and the Super Yang-Mills diagram. II

V. Sahakian, E. Martinec

TL;DR

Problem: Map the finite-temperature phase structure of maximally supersymmetric Yang-Mills on T^p (p≤3) as implied by M-theory dualities. Approach: use a unified framework combining Maldacena duality, Matrix theory, dualities among D-branes, and Horowitz-Polchinski correspondence to relate perturbative SYM, near-horizon brane geometries, and light-cone M-theory; derive phase boundaries by comparing Gibbs energies via localization transitions and HP correspondences. Contributions: explicit phase diagrams for T^1, T^2, and T^3 showing six thermodynamic phases, identification of self-dual points at V around 1, and triple points; demonstration that the Matrix conjecture is a special case of Maldacena's conjecture. Significance: provides a geometrical, duality-guided map of nonperturbative M-theory thermodynamics encoded in SYM, clarifying how different descriptions are related and enabling systematic predictions across regimes.

Abstract

The complete phase diagram of objects in M-theory compactified on tori $T^p$, $p=1,2,3$, is elaborated. Phase transitions occur when the object localizes on cycle(s) (the Gregory-Laflamme transition), or when the area of the localized part of the horizon becomes one in string units (the Horowitz-Polchinski correspondence point). The low-energy, near-horizon geometry that governs a given phase can match onto a variety of asymptotic regimes. The analysis makes it clear that the matrix conjecture is a special case of the Maldacena conjecture.

Black Holes and the Super Yang-Mills diagram. II

TL;DR

Problem: Map the finite-temperature phase structure of maximally supersymmetric Yang-Mills on T^p (p≤3) as implied by M-theory dualities. Approach: use a unified framework combining Maldacena duality, Matrix theory, dualities among D-branes, and Horowitz-Polchinski correspondence to relate perturbative SYM, near-horizon brane geometries, and light-cone M-theory; derive phase boundaries by comparing Gibbs energies via localization transitions and HP correspondences. Contributions: explicit phase diagrams for T^1, T^2, and T^3 showing six thermodynamic phases, identification of self-dual points at V around 1, and triple points; demonstration that the Matrix conjecture is a special case of Maldacena's conjecture. Significance: provides a geometrical, duality-guided map of nonperturbative M-theory thermodynamics encoded in SYM, clarifying how different descriptions are related and enabling systematic predictions across regimes.

Abstract

The complete phase diagram of objects in M-theory compactified on tori , , is elaborated. Phase transitions occur when the object localizes on cycle(s) (the Gregory-Laflamme transition), or when the area of the localized part of the horizon becomes one in string units (the Horowitz-Polchinski correspondence point). The low-energy, near-horizon geometry that governs a given phase can match onto a variety of asymptotic regimes. The analysis makes it clear that the matrix conjecture is a special case of the Maldacena conjecture.

Paper Structure

This paper contains 10 sections, 55 equations, 3 figures.

Table of Contents

  1. Introduction and summary
  2. The details
  3. Stretched and smeared geometries
  4. Localized geometries
  5. Perturbative $p+1$D SYM
  6. Comments on correspondence curves
  7. Specialized treatments: $p=1$
  8. Specialized treatements: $p=2$
  9. Specialized treatements: $p=3$
  10. The final picture

Figures (3)

  • Figure 1: Phase diagram of Light Cone M theory on $T^1$; $S$ is entropy, $V$ is the radius of the circle in Planck units, $N$ is the longitudinal momentum. The geometry label dictionary is as follows: D0: black D0; $\overline{D0}$: black D0 smeared on $V$; D1: black D1; F1: black IIB string; W10: black IIA wave; W11: $11$D black wave; $\overline{W11}$: $11$D black wave smeared on $V$; $10$D BH: IIA LC black hole; $11$D BH: LC M-theory black hole; $\overline{11D}$ BH: LC M-theory BH smeared on $V$. $M$, $T$ and $S$ stand for respectively an M-duality (such as reduction, lift or M flip on $T^3$), a T-duality curve, and an S duality transition.
  • Figure 2: Phase diagram of Light Cone M theory on $T^2$; $V$ is the radius of the circle in Planck units. The geometry label dictionary is as follows: D0: black D0; $\overline{D0}$: black D0 smeared on $V$; D2: black D2; M2: black membrane; $\overline{M2}$: black membrane smeared on a dual circle; WB: black IIB wave; $\overline{WB}$: black IIB wave smeared on a dual circle; W11: $11$D black wave; $\overline{W11}$: $11$D black wave smeared on $V$; $11$D BH: light cone M-theory black hole; $\overline{11D}$ BH: light cone M-theory black hole smeared on $V$; $10$D BH: IIB light cone black hole; $\overline{10D}$ BH: IIB light cone black hole smeared on a dual circle.
  • Figure 3: Phase diagram of Light Cone M theory on $T^3$. D0: black D0; $\overline{D0}$: black D0 smeared on $V$; D3: black D3; W11: $11$D black wave; $\overline{W11}$: $11$D black wave smeared on $V$; $11$D BH: light cone M-theory black hole; $\overline{11D}$ BH: light cone M-theory black hole smeared on $V$.