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Comments on deconfinement in AdS/CFT

Sunjin Choi, Joonho Kim, Seok Kim, June Nahmgoong

TL;DR

The problem is to understand BPS black hole microstates in AdS5×S5 by studying the index of N=4 SYM on S^3×R. The authors extend the large-N index to complex fugacities and analyze the confining saddle to obtain an upper bound on the deconfinement temperature, revealing a Hagedorn-like threshold. They find that this bound lies below the Hawking-Page temperature of known analytic BPS black holes, implying the existence of new, possibly hairy, BPS black holes in AdS5×S5. The Cardy-like high-temperature analysis reproduces a growth of log Z that scales as N^2/ω^2, consistent with bulk entropy function expectations and black hole counting. Overall, the work links gauge theory indices to gravity phase structure and motivates locating new bulk saddle points to realize deconfinement in the BPS sector.

Abstract

We study the index of $\mathcal{N}=4$ Yang-Mills theory on $S^3\times\mathbb{R}$. We argue that the index should undergo a large $N$ deconfinement phase transition, by computing an upper bound of its `temperature.' We compute this bound by optimizing the phases of fugacities. The bound we find has some features analogous to the Hagedorn temperature. We briefly discuss a possible mechanism of the actual deconfinement transition below our bound. Our upper bound is lower than the Hawking-Page transition `temperature' of known BPS black holes in the AdS$_5$ dual. We thus expect the existence of new black holes.

Comments on deconfinement in AdS/CFT

TL;DR

The problem is to understand BPS black hole microstates in AdS5×S5 by studying the index of N=4 SYM on S^3×R. The authors extend the large-N index to complex fugacities and analyze the confining saddle to obtain an upper bound on the deconfinement temperature, revealing a Hagedorn-like threshold. They find that this bound lies below the Hawking-Page temperature of known analytic BPS black holes, implying the existence of new, possibly hairy, BPS black holes in AdS5×S5. The Cardy-like high-temperature analysis reproduces a growth of log Z that scales as N^2/ω^2, consistent with bulk entropy function expectations and black hole counting. Overall, the work links gauge theory indices to gravity phase structure and motivates locating new bulk saddle points to realize deconfinement in the BPS sector.

Abstract

We study the index of Yang-Mills theory on . We argue that the index should undergo a large deconfinement phase transition, by computing an upper bound of its `temperature.' We compute this bound by optimizing the phases of fugacities. The bound we find has some features analogous to the Hagedorn temperature. We briefly discuss a possible mechanism of the actual deconfinement transition below our bound. Our upper bound is lower than the Hawking-Page transition `temperature' of known BPS black holes in the AdS dual. We thus expect the existence of new black holes.

Paper Structure

This paper contains 6 sections, 32 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The large $N$ index at complex fugacities
  3. Instability of the confining saddle point
  4. Cardy limit revisited
  5. Comments on deconfinement
  6. Discussions

Figures (2)

  • Figure 1: Contour plot of ${\rm Re}(f)$ on the $x$-$\phi$ space. The red line shows the curve ${\rm Re}(f)=0$.
  • Figure 2: [left] Charge vs. temperature. There are small and large black hole branches, with negative/positive specific heat, respectively. [right] Temperature vs. free energy. The upper curve for is small black holes with positive free energy, always losing against thermal AdS gravitons. The lower curve is for large black holes, dominating for $\omega<\omega_{\rm HP}^{\rm known}$ with $F<0$.