Disorder in the Sachdev-Yee-Kitaev Model

We give qualitative arguments for the mesoscopic nature of the Sachdev-Yee-Kitaev (SYK) model in the holographic regime with $q^2/N\ll 1$ with $N$ Majorana particles coupled by antisymmetric and random interactions of range $q$. Using a stochastic deformation of the SYK model, we show that its characteristic determinant obeys a viscid Burgers equation with a small spectral viscosity in the opposite regime with $q/N=1/2$, in leading order. The stochastic evolution of the SYK model can be mapped onto that of random matrix theory, with universal Airy oscillations at the edges. A spectral hydrodynamical estimate for the relaxation of the collective modes is made.Comment: 7 pages, 1 figur

QCD, diffraction and string theory

Recently, string theory on some specific curved backgroud spacetime geometries has been conjectured to be equivalent to certain gauge theories (AdS/CFT correspondence). This correspondence may be used to investigate the non-perturbative regime of gauge theories. I describe its application to the study of soft scattering amplitudes in a confining gauge theory. I describe two qualitatively different applications: amplitudes with vacuum quantum number exchange (Pomeron-like), amplitudes with Reggeon exchange. The last case requires going beyond eikonal approximation on the gauge theory side.Comment: 5 pages. Presented at the 10th International Workshop on Deep Inelastic Scattering, DIS2002, Krakow, Polan

Spin-Spin and Spin-Orbit Interactions in Strongly Coupled Gauge Theories

We evaluate the spin-orbit and spin-spin interaction between two fermions in strongly coupled gauge theories in their Coulomb phase. We use the quasi-instantaneous character of Coulomb's law at strong coupling to resum a class of ladder diagrams. For ${\cal N}=4$ SYM we derive both weak and strong coupling limits of the the spin-orbit and spin-spin interactions, and find that in the latter case these interactions are subleading corrections and do not seriously affect the deeply bound Coulomb states with large angular momentum, pointed out in our previous paper. The results are important for understanding of the regime of intermediate coupling, which is the case for QCD somewhat above the chiral transition temperature

Stress Tensor of Static Dipoles in strongly coupled N\cal{N}=4 Gauge Theory

In the context of the AdS/CFT correspondence we calculate the induced stress tensor of static dipoles (electric-electric and electric-magnetic) in a strongly coupled ${\cal N}=4$ SYM gauge theory, by solving the linearized Einstein equation with Maldecena string as a source. Analytic expressions are given for the far-field and a near-field close to one charge, and compared to what one has in weak coupling. The result can be compared to lattice results for QCD-like theories in a deconfined but strongly coupled regime

On Heavy-Quark Free Energies, Entropies, Polyakov Loop, and AdS/QCD

In this paper we explore some of the features of a heavy quark-antiquark pair at finite temperature using a five-dimensional framework nowadays known as AdS/QCD. We shall show that the resulting behavior is consistent with our qualitative expectations of thermal gauge theory. Some of the results are in good agreement with the lattice data that provides additional evidence for the validity of the proposed model.Comment: 15 pages, 10 figures; v2: comments added, misprints correcte