Classical/quantum integrability in AdS/CFT

We study SU(N ) plane-wave matrix theory up to fourth perturbative order in its large N planar limit. The effective Hamiltonian in the closed su(2) subsector of the model is explicitly computed through a specially tailored computer program to perform large scale distributed symbolic algebra and generation of planar graphs. The number of graphs here was in the deep billions. The outcome of our computation establishes the four-loop integrability of the planar plane-wave matrix model. To elucidate the integrable structure we apply the recent technology of the perturbative asymptotic Bethe ansatz to our model. The resulting S-matrix turns out to be structurally similar but nevertheless distinct to the so far considered long-range spin-chain S-matrices of Inozemtsev, Beisert-Dippel-Staudacher and Arutyunov-Frolov-Staudacher in the AdS/CFT context. In particular our result displays a breakdown of BMN scaling at the four-loop order. That is, while there exists an appropriate identification of the matrix theory mass parameter with the coupling constant of the N = 4 superconformal Yang-Mills theory which yields an eighth order lattice derivative for well separated impurities (naively implying BMN scaling) the detailed impurity contact interactions ruin this scaling property at the four-loop order. Moreover we study the issue of "wrapping" interactions, which show up for the first time at this loop-order through a Konishi descendant length four operator.

Section: Introductionsupporting

confidence: 58%

Planar plane-wave matrix theory at the four loop order: Integrability without BMN scaling

Fischbacher

Klose

Plefka

2005

“…The finite size Bethe ansatz equations that we have obtained, including the 1/L correction, may allow for a comparison with the string dynamics along the lines of [26,27,28].…”

Section: Discussionmentioning

confidence: 97%

Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings

Hernández

López

Periáñez

et al. 2005

N = 4 supersymmetric Yang-Mills operators carrying large charges are dual to semiclassical strings in AdS 5 × S 5 . The spectrum of anomalous dimensions of very large operators has been calculated solving the Bethe ansatz equations in the thermodynamic limit, and matched to energies of string solitons. We have considered finite size corrections to the Bethe equations, that should correspond to quantum effects on the string side.

“…Generalization of our results for any A (1) n (n > 1) ATFT will be also presented in a separate publication. Finally, a similar exhaustive analysis regarding principal chiral models (partial results maybe found in [46]) will be particularly relevant especially bearing in mind the physical significance of a specific super-symmetric principal chiral model within the AdS/CFT correspondence [47,48]. Also define the fundamental weights µ k = (µ 1 k , .…”

Section: Discussionmentioning

confidence: 99%

A_n⁽¹⁾affine Toda field theories with integrable boundary conditions revisited

Doikou¹

2008

Generic classically integrable boundary conditions for the A (1) n affine Toda field theories (ATFT) are investigated. The present analysis rests primarily on the underlying algebra, defined by the classical version of the reflection equation. We use as a prototype example the first non-trivial model of the hierarchy i.e. the A (1) 2 ATFT, however our results may be generalized for any A (1) n (n > 1). We assume here two distinct types of boundary conditions called some times soliton preserving (SP), and soliton non-preserving (SNP) associated to two distinct algebras, i.e. the reflection algebra and the (q) twisted Yangian respectively. The boundary local integrals of motion are then systematically extracted from the asymptotic expansion of the associated transfer matrix. In the case of SNP boundary conditions we recover previously known results. The other type of boundary conditions (SP), associated to the reflection algebra, are novel in this context and lead to a different set of conserved quantities that depend on free boundary parameters. It also turns out that the number of local integrals of motions for SP boundary conditions is 'double' compared to those of the SNP case.