Yangian symmetry, S‐matrices and Bethe ansatz for the AdS₅ × S⁵ superstring

Abstract

We discuss the relation between the recently derived bound state S-matrices for the AdS5 × S 5 superstring and Yangian symmetry. We will study the relation between this Yangian symmetry and the Bethe ansatz. In particular we can use it to derive the Bethe equations for bound states.

Wrapping effects in supersymmetric gauge theories

“…The so-called Y-system [55][56][57][58] is a set of functional equations proposed to describe the full spectrum of N = 4 SYM, comprehensive of wrapping effects on short operators. It can be derived from the thermodynamic Bethe ansatz approach [44][45][46][47][48][49][50][51][52]. In [55] it was applied to find the four-loop anomalous dimension of the Konishi operator, and the result was found to be in agreement with the previous computations [19][20][21]64].…”

“…The Lüscher method has been used to analyze wrapping contributions also on different operators [38][39][40] on the gauge side, even beyond the critical order [41], but its generalization to arbitrary states is very difficult, and thus alternative approaches have been attempted. In particular, a great progress has been made towards a general description of finite-size effects in terms of integrable structures, both on the gauge and on the string side, by means of the thermodynamic Bethe ansatz [42][43][44][45][46][47][48][49][50][51][52][53][54], which led to the formulation of the Y-system approach [55][56][57][58][59]. These techniques have been then applied to compute wrapping effects at strong coupling in the CFT [60,61].…”

“…The thermodynamic Bethe ansatz [42] is an extension of the standard Bethe ansatz method that allows to study systems at finite temperature in the thermodynamic limit. Its relevance in the context of finite-size interactions relies on the general idea originally developed in [43], and then recently applied to the AdS/CFT correspondence [25,[44][45][46][47][48][49][50][51][52][53][54].…”

“…The Lüscher approach was successfully applied to the study of wrapping corrections in several other situations [25,[38][39][40], and to the computation of the five-loop anomalous dimension of the Konishi operator [41], but it is difficult to generalize it to deal with generic states. More recently, some proposals appeared for a general description of finite-size effects, based on the thermodynamic Bethe ansatz [42][43][44][45][46][47][48][49][50][51][52][53][54], from which the so-called Y-system [55][56][57][58][59] has been derived. The new techniques successfully reproduce the known wrapping contribution to the Konishi anomalous dimension, and have also been applied to analyze explicitly wrapping effects at strong coupling in the CFT [60][61][62][63].…”

Nonlocal symmetries and factorized scattering

“…and thus we conclude that the Yangian level-0 constraints fix the S-matrix up to two degrees of freedom corresponding to two Casimirs of su(2|2). Note that the construction of the Casimirs from a Killing form κ ab of the algebra is non-trivial since the latter vanishes, see [42].…”