Unraveling AdS/CFT

In this review, I survey the conjectured correspondence between a string theory in ten dimensions and certain supersymmetric gauge theories in four. This duality has recently garnered considerable attention from scientists studying the hot matter produced in heavy-ion collisions. An important and immediate question is to what extent one can hope to describe the dynamics of the quark–gluon plasma in a supersymmetric conformal field theory. Here I explain recent applications of the AdS/CFT correspondence to the strongly interacting matter produced at the Relativistic Heavy Ion Collider. Progress in characterizing the medium with these techniques will be discussed, as well as limitations inherent to the method.     

The Hopf superalgebra of AdS/CFT

We describe the unconventional infinite-dimensional Hopf superalgebra related to the integrable S-matrix of the AdS/CFT correspondence, and discuss its typical and atypical representations.     

The AdS/CFT Correspondence and Holographic QCD

Holographic QCD is an extra-dimensional approach to modeling QCD resonances and their interactions. Holographic models encode information about chiral symmetry breaking, Weinberg sum rules, vector meson dominance, and other phenomenological features of QCD. There are two complementary approaches to holographic model building: a top–down approach which begins with string-theory brane configurations, and a bottom–up approach which is more phenomenological. In this talk I will describe the AdS/CFT correspondence, which motivates Holographic QCD, and the techniques used to build holographic models of QCD and to calculate observables in those models. I will also discuss an intriguing lightcone approach to Holographic QCD discovered by Brodsky and De Teramond.     

Brick walls and AdS/CFT

We discuss the relationship between the bulk-boundary correspondence in Rehren’s algebraic holography (and in other ‘fixed-background’, QFT-based, approaches to holography) and in mainstream string-theoretic ‘Maldacena AdS/CFT’. Especially, we contrast the understanding of black-hole entropy from the point of view of QFT in curved spacetime—in the framework of ’t Hooft’s ‘brick wall’ model—with the understanding based on Maldacena AdS/CFT. We show that the brick-wall modification of a Klein–Gordon field in the Hartle–Hawking–Israel state on $1+2$ dimensional Schwarzschild AdS has a well-defined boundary limit with the same temperature and entropy as the brick-wall-modified bulk theory. One of our main purposes is to point out a close connection, for general AdS/CFT situations, between the puzzle raised by Arnsdorf and Smolin regarding the relationship between Rehren’s algebraic holography and mainstream AdS/CFT and the puzzle embodied in the ‘complementarity principle’ proposed by Mukohyama and Israel in their work on the brick-wall approach to black hole entropy. Working on the assumption that similar results will hold for bulk QFT other than the Klein–Gordon field and for Schwarzschild AdS in other dimensions, and recalling the first author’s proposed resolution to the Mukohyama–Israel puzzle based on his ‘matter–gravity entanglement hypothesis’, we argue that, in Maldacena AdS/CFT, the algebra of the boundary CFT is isomorphic only to a proper subalgebra of the bulk algebra, albeit (at non-zero temperature) the (GNS) Hilbert spaces of bulk and boundary theories are still the ‘same’—the total bulk state being pure, while the boundary state is mixed (thermal). We also argue from the finiteness of its boundary (and hence, on our assumptions, also bulk) entropy at finite temperature, that the Rehren dual of the Maldacena boundary CFT cannot itself be a QFT and must, instead, presumably be something like a string theory.     

Semiclassical integrability in AdS/CFT

Integrable structures on both sides of the AdS/CFT correspondence are reviewed, with emphasis on the Bethe ansatz. To cite this article: K. Zarembo, C. R. Physique 5 (2004).

Résumé

Des structures intégrables de chaque coté de la correspondance AdS/CFT sont rappelées, avec un accent sur la conjecture de Bethe. Pour citer cet article : K. Zarembo, C. R. Physique 5 (2004).     

AdS/CFT Correspondence and Dark Soliton

In this paper we use the AdS/CFT correspondence to study dark soliton solutions in a holographic model of a relativistic superfluid. We calculate the length scales corresponding to the condensate and the charge density depletion, and find relation with the chemical potential. We compare our solutions with the quasiparticle excitations above the holographic superfluid and find that the scale of the excitations is comparable to the soliton coherence length scales.     

Five loop Konishi from AdS/CFT

We derive the perturbative five loop anomalous dimension of the Konishi operator in N=4$N=4$ SYM theory from the integrable string sigma model by evaluating finite size effects using Lüscher formulas adapted to multimagnon states at weak coupling. In addition, we derive the five loop wrapping contribution for the L=2$L=2$ 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.     

Numerical metric extraction in AdS/CFT

An iterative method for recovering the bulk information in asymptotically AdS spacetimes is presented. We consider zero energy spacelike geodesics and their relation to the entanglement entropy in three dimensions to determine the metric in certain symmetric cases. A number of comparisons are made with an alternative extraction method presented in arXiv:hep-th/0609202, and the two methods are then combined to allow metric recovery in the most general type of static, spherically symmetric setups. We conclude by extracting the mass and density profiles for a toy model example of a gas of radiation in (2 + 1)-dimensional AdS.     

Applications of the AdS/CFT correspondence

In this writeup of a talk delivered at the Lepton Photon Conference 2011, applications of the AdS/CFT correspondence in diverse areas of physics are reviewed.     

Non-equilibrium phase transition from AdS/CFT

Using AdS/CFT correspondence we study a non-equilibrium phase transition in the presence of a constant external magnetic field. The transition occurs when the sign of the differential conductivity reverses. Utilizing numerical method we show that the type of the transition depends on the value of magnetic field as well as the temperature of the gauge theory. Moreover we show that this transition does not depend on supersymmetry preserved by the system at zero temperature and the dimension of the subspace on which the fundamental matter field lives.     

Saturating the unitarity bound in AdS/CFT(AdS)

Journal of High Energy Physics - Generalized Bogomolny equations are encountered in the localization of the topological $ \mathcal{N} = 4\;{\text{SYM}} $ theory. The boundary conditions for...     

Supersymmetry in the AdS/CFT correspondence

We study how local symmetry transformations of (p,q) anti de Sitter supergravities in three dimensions act on fields on the two-dimensional boundary. The boundary transformation laws are shown to be the same as those of two-dimensional (p,q) conformal supergravities for p,q≤2. Weyl and super Weyl transformations are generated from three-dimensional general coordinate and super transformations.     

Hadron spectroscopy and structure from AdS/CFT

The AdS/CFT correspondence between conformal field theory and string states in an extended space-time has provided new insights into not only hadron spectra, but also their light-front wave functions. We show that there is an exact correspondence between the fifth-dimensional coordinate of anti-de Sitter space z and a specific impact variable ζ which measures the separation of the constituents within the hadron in ordinary space-time. This connection allows one to predict the form of the light-front wave functions of mesons and baryons, the fundamental entities which encode hadron properties and scattering amplitudes. A new relativistic Schr?dinger light-front equation is found which reproduces the results obtained using the fifth-dimensional theory. Since they are complete and orthonormal, the AdS/CFT model wave functions can be used as an initial ansatz for a variational treatment or as a basis for the diagonalization of the light-front QCD Hamiltonian. A number of applications of light-front wave functions are also discussed.