Algebraic Curves for Integrable String Backgrounds

Many Ramond-Ramond backgrounds which arise in the AdS/CFT correspondence are described by integrable sigma-models. The equations of motion for classical spinning strings in these backgrounds are exactly solvable by finite-gap integration techniques. We review the finite-gap integral equations and algebraic curves for coset sigma-models, and then apply the results to the AdS(d+1) backgrounds with d=4,3,2,1.Comment: 33 pages, 8 figures, talk at "Gauge Fields. Yesterday, Today, Tomorrow", Moscow, 19-24.01.2010; v2: misprints in (4.8), (4.13) corrected, discussion of the quantum Bethe equations expande

Quiver CFT at strong coupling

The circular Wilson loop in the two-node quiver CFT is computed at large-N and strong 't Hooft coupling by solving the localization matrix model.Comment: 30 pages, 6 figures; v2: misprints correcte

Collective field approach to gauged principal chiral field at large N

The lattice model of principal chiral field interacting with the gauge fields, which have no kinetic term, is considered. This model can be regarded as a strong coupling limit of lattice gauge theory at finite temperature. The complete set of equations for collective field variables is derived in the large N limit and the phase structure of the model is studied.Comment: LaTex (no figures), preprint SMI-94-7, 10 p

String Breaking from Ladder Diagrams in SYM Theory

The AdS/CFT correspondence establishes a string representation for Wilson loops in N=4 SYM theory at large N and large 't Hooft coupling. One of the clearest manifestations of the stringy behaviour in Wilson loop correlators is the string-breaking phase transition. It is shown that resummation of planar diagrams without internal vertices predicts the strong-coupling phase transtion in exactly the same setting in which it arises from the string representation.Comment: 15 pages, 5 figures; v2: misprint in eq. (3.9) corrected; v4: treatment of inhomogeneous term in the Dyson equation modifie

Level Crossing in Random Matrices: I. Random perturbation of a fixed matrix

We consider level crossing in a matrix family $H=H_0+\lambda V$ where $H_0$ is a fixed $N\times N$ matrix and $V$ belongs to one of the standard Gaussian random matrix ensembles. We study the probability distribution of level crossing points in the complex plane of $\lambda$, for which we obtain a number of exact, asymptotic and approximate formulas.Comment: 35 pages, 16 figures; v2: Introduction and sec. 3.3 expanded, refs. adde