Romuald A. Janik

Review of AdS/CFT Integrability: An Overview

This is the introductory chapter of a review collection on integrability in the context of the AdS/CFT correspondence. In the collection, we present an overview of the achievements and the status of this subject as of the year 2010.

The AdS{sub 5}xS{sup 5} superstring worldsheet S matrix and crossing symmetry

An S matrix satisfying the Yang-Baxter equation with symmetries relevant to the AdS{sub 5}xS{sup 5} superstring recently has been determined up to an unknown scalar factor. Such scalar factors are typically fixed using crossing relations; however, due to the lack of conventional relativistic invariance, in this case its determination remained an open problem. In this paper we propose an algebraic way to implement crossing relations for the AdS{sub 5}xS{sup 5} superstring worldsheet S matrix. We base our construction on a Hopf-algebraic formulation of crossing in terms of the antipode and introduce generalized rapidities living on the universal cover of the parameter space which is constructed through an auxillary, coupling-constant dependent, elliptic curve. We determine the crossing transformation and write functional equations for the scalar factor of the S matrix in the generalized rapidity plane.

Wrapping interactions and a new source of corrections to the spin-chain/string duality

Abstract Assuming that the world-sheet sigma-model in the AdS/CFT correspondence is an integrable quantum field theory, we deduce that there might be new corrections to the spin-chain/string Bethe ansatz paradigm. These come from virtual particles propagating around the circumference of the cylinder and render Bethe ansatz quantization conditions only approximate. We determine the nature of these corrections both at weak and at strong coupling in the near-BMN limit, and find that the first corrections behave qualitatively as wrapping interactions at weak coupling.

Asymptotic perfect fluid dynamics as a consequence of AdS/CFT correspondence

We study the dynamics of strongly interacting gauge-theory matter (modelling quark-gluon plasma) in a boost-invariant setting using the AdS/CFT correspondence. Using Fefferman-Graham coordinates and with the help of holographic renormalization, we show that perfect fluid hydrodynamics emerges at large times as the unique nonsingular asymptotic solution of the nonlinear Einstein equations in the bulk. The gravity dual can be interpreted as a black hole moving off in the fifth dimension. Asymptotic solutions different from perfect fluid behaviour can be ruled out by the appearance of curvature singularities in the dual bulk geometry. Subasymptotic deviations from perfect fluid behaviour remain possible within the same framework.

Four-loop perturbative Konishi from strings and finite size effects for multiparticle states

We derive the perturbative four loop anomalous dimension of the Konishi operator in N = 4 SYM theory from the integrable string sigma model by evaluating the finite size effects using Luscher formulas adapted to multimagnon states at weak coupling. We obtain these multiparticle generalizations of Luscher formulas by studying certain exactly solvable relativistic integrable quantum field theories. The final result involves a summation of all bound states in the mirror theory and agrees with gauge theory perturbative computations.

Characteristics of thermalization of boost-invariant plasma from holography

We report on the approach toward the hydrodynamic regime of boost-invariant N=4 super Yang-Mills plasma at strong coupling starting from various far-from-equilibrium states at τ=0. The results are obtained through a numerical solution of Einsteins equations for the dual geometries, as described in detail in the companion article [M. P. Heller, R. A. Janik, and P. Witaszczyk, arXiv:1203.0755]. Despite the very rich far-from-equilibrium evolution, we find surprising regularities in the form of clear correlations between initial entropy and total produced entropy, as well as between initial entropy and the temperature at thermalization, understood as the transition to a hydrodynamic description. For 29 different initial conditions that we consider, hydrodynamics turns out to be definitely applicable for proper times larger than 0.7 in units of inverse temperature at thermalization. We observe a sizable anisotropy in the energy-momentum tensor at thermalization, which is nevertheless entirely due to hydrodynamic effects. This suggests that effective thermalization in heavy-ion collisions may occur significantly earlier than true thermalization.

Four loop twist two, BFKL, wrapping and strings

Abstract The anomalous dimensions of twist two operators have to satisfy certain consistency requirements derived from BFKL. For N = 4 SYM it was shown that at four loops, the anomalous dimensions derived from the all-loop asymptotic Bethe ansatz do not pass this test. In this paper we obtain the remaining wrapping part of these anomalous dimensions from string theory and show that these contributions exactly cure the problem and lead to agreement with both LO and NLO BFKL expectations.

Wrapping interactions at strong coupling: The Giant magnon

We derive generalized Luescher formulas for finite size corrections in a theory with a general dispersion relation. For the AdS{sub 5}xS{sup 5} superstring these formulas encode leading wrapping interaction effects. We apply the generalized {mu}-term formula to calculate finite size corrections to the dispersion relation of the giant magnon at strong coupling. The result exactly agrees with the classical string computation of Arutyunov, Frolov, and Zamaklar. The agreement involved a Borel resummation of all even loop orders of the BES/BHL dressing factor thus providing a strong consistency check for the choice of the dressing factor.

Gauge-gravity duality and thermalization of a boost-invariant perfect fluid

We derive the equation for the quasinormal modes corresponding to the scalar excitation of a black hole moving away in the fifth dimension. This geometry is the AdS/CFT dual of a boost-invariant expanding perfect fluid in N=4 SUSY Yang-Mills theory at large proper-time. On the gauge-theory side, the dominant solution of the equation describes the decay back to equilibrium of a scalar excitation of the perfect fluid. Its characteristic proper-time can be interpreted as a thermalization time of the perfect fluid, which is a universal (and numerically small) constant in units of the unique scale of the problem. This may provide a new insight on the short thermalization-time puzzle encountered in heavy-ion collision phenomenology. A nontrivial scaling behavior in proper-time is obtained which can be interpreted in terms of a slowly varying adiabatic approximation.

Five loop Konishi from AdS/CFT

Abstract We derive the perturbative five loop anomalous dimension of the Konishi operator in N = 4 SYM theory from the integrable string sigma model by evaluating finite size effects using Luscher formulas adapted to multimagnon states at weak coupling. In addition, we derive the five loop wrapping contribution for the L = 2 single impurity state in the β deformed theory, which may be within reach of a direct perturbative computation. The Konishi expression exhibits two new features — a modification of Asymptotic Bethe Ansatz quantization and sensitiveness to an infinite set of coefficients of the BES/BHL dressing phase. The result satisfies nontrivial self-consistency conditions — simple transcendentality structure and cancellation of μ -term poles. It may be a testing ground for the proposed AdS/CFT TBA systems.