Strongly coupled N=4 supersymmetric Yang-Mills plasma on the Coulomb branch. I. Thermodynamics

Kiminad A Mamo

doi:10.1103/physrevd.100.066010

Abstract

We study $\mathcal{N} = 4$ super Yang-Mills theory on the Coulomb branch (cSYM) in the strong coupling limit by using the AdS/CFT correspondence. The dual geometry is the rotating black 3-brane Type IIB supergravity solution with a single non-zero rotation parameter $r_{0}$ which sets a fixed mass scale corresponding to the scalar condensate $<\mathcal{O}>\,\,\sim r_{0}^4$ in the Coulomb branch. We introduce a new ensemble where $T$ and $<\mathcal{O}>$ are held fixed, i.e., the free energy $F(T,<\mathcal{O}>)$ is a function of $T$ and $<\mathcal{O}>$. We compute the equation of state (EoS) of $\mathcal{N} = 4$ cSYM at finite $T$, as well as the heavy quark-antiquark potential and the quantized mass spectrums of the scalar and spin-2 glueballs at $T=0$. By computing the Wilson loop (minimal surface) at $T=0$, we determine the heavy quark-antiquark potential $V(L)$ to be the Cornell potential, which is confining for large separation $L$. At $T\neq 0$, we find two black hole branches: the large black hole and small black hole branches. For the large black hole branch, that has positive specific heat, we find qualitatively similar EoS to that of pure Yang-Mills theory on the lattice. For the small black hole branch, that has negative specific heat, we find an EoS where the entropy and energy densities decrease with $T$. We also find a second-order phase transition between the large and small black hole branches with critical temperature $T_c=T_{min}$.

Highlights

The AdS=CFT correspondence [1,2,3] has opened a new window to the strongly coupled regime of gauge theories such as N 1⁄4 4 super Yang-Mills (SYM)
Among various Type IIB supergravity background solutions that are dual to the strongly coupled N 1⁄4 4 cSYM at zero temperature [19,20,21,22], in this paper, we will study a Type IIB supergravity background solution that describes nonextremal rotating black 3-branes which, in the extremal limit, i.e., r0 ≫ m1=4, is dual to N 1⁄4 4 SYM on the Coulomb branch at zero temperature that arises from Nc D3-branes distributed uniformly in the angular direction, inside a 3-sphere of radius r0 [20]
IV, we study the mass spectrum of glueballs in N 1⁄4 4 cSYM

Summary

INTRODUCTION

The AdS=CFT correspondence [1,2,3] has opened a new window to the strongly coupled regime of gauge theories such as N 1⁄4 4 super Yang-Mills (SYM). We should note that having an imaginary gauge potential, in our ensemble, does not lead to any inconsistencies, since all physical quantities in the 5-dimensional spacetime are given in terms of ð∂rA1t Þ2. Using (1.1) for fixed hOi ∼ Λ4, the corresponding free energy density fðT; ΛÞ of our ensemble can be determined by integrating the entropy density sðT; ΛÞ as [9,12]. As a comparison to N 1⁄4 4 cSYM, we have plotted, see Fig. 3, the free energy density of N 1⁄4 4 SYM on sphere fsphere, which is given by [16], see [47],. Note that we have a factor of 2 in (3.4) because our gauge covers only half of the full string configuration which accounts to only half of the full potential energy between the quarks; see [47] for discussion on how to compute VðLÞ in the xðrÞ gauge instead of the widely used rðxÞ gauge of [48]

R2 3 rm with x0

CONCLUSION