Black hole-black string phase transitions in thermal 1+1-dimensional supersymmetric Yang-Mills theory on a circle

TL;DR

The paper connects the Gregory-Laflamme black hole–black string transition in gravity to a thermal phase transition in large-N 1+1D maximally supersymmetric Yang-Mills on a circle, uniting strong- and weak-coupling analyses via holography. At strong coupling, the transition is read from gravity through GL instabilities and the behavior of Wilson loop order parameters, while at weak coupling it emerges in a reduced 0+1D bosonic matrix model and a subsequent LG description, validated by Monte Carlo simulations. The results indicate a consistent picture across couplings, with a first-order transition at strong coupling and a closely related, cusp-adjacent transition at weak coupling that can be captured by a simple Landau-Ginzburg form, suggesting a shared universality class. Extensions to high-temperature reductions, symmetric product CFT limits, and Matrix String Theory further illuminate the phase structure and dual descriptions of D0-brane dynamics on a circle.

Abstract

We review and extend earlier work that uses the AdS/CFT correspondence to relate the black hole-black string transition of gravitational theories on a circle to a phase transition in maximally supersymmetric 1+1-dimensional SU(N) gauge theories at large N, again compactified on a circle. We perform gravity calculations to determine a likely phase diagram for the strongly coupled gauge theory. We then directly study the phase structure of the same gauge theory, now at weak 't Hooft coupling. In the interesting temperature regime for the phase transition, we may reduce the 1+1-dimensional theory to a 0+1-dimensional bosonic theory, which we solve using Monte Carlo methods. We find strong evidence that the weakly coupled gauge theory also exhibits a black hole-black string like phase transition in the large N limit. We demonstrate that a simple Landau-Ginzburg like model describes the behaviour near the phase transition remarkably well. The weak coupling transition appears to be close to the cusp between a first order and a second order transition.

Figures (11)

• Figure 1: An educated guess for the free energy as a function of temperature for black holes, uniform black strings, and non-uniform black strings in 10 dimensions. Appendix B shows that the non-uniform solutions have less favoured free energy than the uniform solutions near $t_{GL}$. Analogy with $d = 6$ indicates that the non-uniform and localized phases may meet at a topology changing solution. Dashed lines represent phases conjectured to be unstable.
• Figure 2: Monte Carlo determination of the saddle point eigenvalue distribution of $\psi^A$ for the matrix integral (\ref{['eq:matrixintegral']}) with $N = 20$.
• Figure 3: Eigenvalue distribution of $P_x$ for various values of $\lambda' t$ with $N=12$. A phase transition appears to occur for $\lambda' t \simeq 1.4$, and for this value we compare with $(1 + \cos{\theta})/(2 \pi)$, the transition distribution for our $b = 0$ Landau-Ginzburg model discussed in section \ref{['sec:LGanal']}.
• Figure 4: The first Fourier mode $u_1$ of the eigenvalue distribution of $P_x$ as a function of $\lambda' t$, for various values of $N$. To the left of the transition at $\lambda' t \simeq 1.4$, the values remain approximately invariant as $N$ increases. To the right, $u_1$ decreases consistent with going to zero in the large $N$ limit as $1/N$. Statistical error bars are smaller than the plot symbols.
• Figure 5: The second Fourier mode $u_2$ of the eigenvalue distribution of $P_x$ as a function of $\lambda' t$ for various values of $N$. For large $N$ the gradient appears to become discontinuous at the transition.