The equilibrium thermodynamic properties of the $\mathrm{SU}(N)$ plasma are studied nonperturbatively in the large-$N$ limit, via high-precision lattice simulations at temperatures from $0.8{T}_{c}$ to $3.4{T}_{c}$ (${T}_{c}$ being the critical deconfinement temperature). Our results for $\mathrm{SU}(N)$ Yang-Mills theories with $N=3$, $4$, $5$, $6$, and $8$ colors show a very mild dependence on $N$, supporting the idea that the QCD plasma could be described by models based on the large-$N$ limit. We compare our data with various theoretical descriptions, including, in particular, the improved holographic QCD model proposed by Kiritsis and collaborators. We also comment on the relevance of an AdS/CFT description in a phenomenologically interesting temperature range where the system, while still strongly coupled, becomes approximately scale invariant. Finally, we extrapolate our results to the $N\ensuremath{\rightarrow}\ensuremath{\infty}$ limit.

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Thermodynamics of the QCD Plasma and the Large-N Limit

This report is the result of the collaboration and research effort of the Quarkonium Working Group over the last three years. It provides a comprehensive overview of the state of the art in heavy-quarkonium theory and experiment, covering quarkonium spectroscopy, decay, and production, the determination of QCD parameters from quarkonium observables, quarkonia in media, and the effects on quarkonia of physics beyond the Standard Model. An introduction to common theoretical and experimental tools is included. Future opportunities for research in quarkonium physics are also discussed.

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Heavy quarkonium physics

SU(N) gauge theories at large N

The theory of the strong interaction, quantum chromodynamics (QCD), describes the generation of hadronic masses and the state of hadronic matter during the early stages of the evolution of the universe. As a complement, experiments with ultracold fermionic atoms provide a clean environment to benchmark our understanding of dynamical formation of condensates and the generation of bound states in strongly interacting many-body systems. Renormalization Group (RG) techniques offer great potential for theoretical advances in both hot and dense QCD and many-body physics, but their connections have not yet been investigated in great detail. We aim to take a further step to bridge this gap. A cross-fertilization is indeed promising since it may eventually provide us with an ab initio description of hadronization, condensation and bound-state formation in strongly interacting theories. After giving a thorough introduction to the derivation and analysis of fermionic RG flows, we give an introductory review of our present understanding of universal long-range behavior in various different theories, ranging from non-relativistic many-body problems to relativistic gauge theories, with an emphasis on scaling behavior of physical observables close to quantum phase transitions (i.e. phase transitions at zero temperature) as well as thermal phase transitions.

http://iopscience.iop.org/article/10.1088/0954-3899/39/3/033001/pdf

Fermion interactions and universal behavior in strongly interacting theories

In the presence of a static quark-antiquark pair, the spectrum of the low- lying states in SU(N) gauge theories is discrete and likely to be described, at large quark separations r, by an efiective string theory. The expansion of the excitation energies in powers of 1=r, which derives from the latter, involves an increasing number of unknown couplings that characterize the string self-interactions. Using open{closed string duality, we show that the possible values of the couplings are constrained by a set of algebraic relations. In particular, the corrections of order 1=r 2 must vanish, while the 1=r 3 terms (whichweworkoutforthefewlowest levels) dependonasingleadjustablecouplingonly.

/pdf/string-excitation-energies-in-su-n-gauge-theories-beyond-the-3hfb2tww6d.pdf

String excitation energies in SU(N) gauge theories beyond the free-string approximation

https://arxiv.org/pdf/hep-lat/0312022.pdf

The deconfinement phase transition of Sp(2) and Sp(3) Yang-Mills theories in 2+1 and 3+1 dimensions

We report on a very accurate measurement of the static quark potential in SU(2) Yang-Mills theory in (2+1) dimensions in order to study the corrections to the linear behaviour. We perform numerical simulations at zero and finite temperature comparing our results with the corrections given by the effective string picture in these two regimes. We also check for universal features discussing our results together with those recently published for the (2+1)-d (2) and SU(3) pure gauge theories.

Static quark potential and effective string corrections in the (2+1)-d SU(2) Yang-Mills theory

$D$-theory provides an alternative lattice regularization of the 2D $\mathrm{C}\mathrm{P}(N\ensuremath{-}1)$ quantum field theory in which continuous classical fields emerge from the dimensional reduction of discrete $\mathrm{S}\mathrm{U}(N)$ quantum spins. Spin ladders consisting of $n$ transversely coupled spin chains lead to a $\mathrm{C}\mathrm{P}(N\ensuremath{-}1)$ model with a vacuum angle $\ensuremath{\theta}=n\ensuremath{\pi}$. In $D$-theory no sign problem arises and an efficient cluster algorithm is used to investigate $\ensuremath{\theta}$-vacuum effects. At $\ensuremath{\theta}=\ensuremath{\pi}$ there is a first order phase transition with spontaneous breaking of charge conjugation symmetry for $\mathrm{C}\mathrm{P}(N\ensuremath{-}1)$ models with $Ng2$.

Study of CP(N-1) theta-vacua by cluster simulation of SU(N) quantum spin ladders.

The long-range forces between holes in an antiferromagnet are due to
magnon exchange. The one-magnon exchange potential between two holes is 
proportional to cos(2 ϕ)/r
 2 where r is the distance 
vector of the holes and ϕ is the angle between r and an axis of 
the square crystal lattice. One-magnon exchange leads to bound states of holes 
with antiparallel spins resembling d-wave symmetry.

/pdf/magnon-mediated-binding-between-holes-in-an-antiferromagnet-3stya9zrbl.pdf

Magnon-mediated binding between holes in an antiferromagnet

We present numerical results for the deconfinement phase transition in Sp(2) and Sp(3) Yang-Mills theories in (2+1)-D and (3+1)-D. We then make a conjecture on the order of this phase transition in Yang-Mills theories with general Lie groups G = SU(N), SO(N), Sp(N) and with exceptional groups G = G(2), F(4), E(6), E(7), E(8).

M. Pepe

Papers

The deconfinement phase transition of Sp(2) and Sp(3) Yang-Mills theories in 2+1 and 3+1 dimensions

Static quark potential and effective string corrections in the (2+1)-d SU(2) Yang-Mills theory

Study of CP(N-1) theta-vacua by cluster simulation of SU(N) quantum spin ladders.

Magnon-mediated binding between holes in an antiferromagnet

Thedeconfinement phase transition in Yang-Mills theory with general Lie group G