The strong coupling limit of the scaling function from the quantum string Bethe ansatz

Abstract

Using the quantum string Bethe ansatz we derive the one-loop energy of a folded string rotating with angular momenta (S, J) in AdS 3 × S 1 ⊂ AdS 5 × S 5 in the limit 1 ≪ J ≪ S, z = √ λ log(S/J)/(πJ) fixed. The one-loop energy is a sum of two contributions, one originating from the Hernandez-Lopez phase and another one being due to spin chain finite size effects. We find a result which at the functional level exactly matches the result of a string theory computation. Expanding the result for large z we obtain the strong coupling limit of the scaling function for low twist, high spin operators of the SL(2) sector of N = 4 SYM. In particular we recover the famous − 3 log(2) π . Its appearance is a result of non-trivial cancellations between the finite size effects and the Hernandez-Lopez correction.

A generalized scaling function for AdS/CFT

“…If we were to again expand in small j via (1.21) we would find j 2 log j terms. The result (1.24) was fully derived in [24] from the asymptotic Bethe ansatz [7,5] with approximate strong coupling (AFS + HL [28]) dressing phase. Once again, this is an important cross-check on the consistency of the extraction of the one-loop correction of the dressing phase from one-loop string theory [28,29], see also the very recent derivation [30], but does not answer the question how the dimensions of the gauge theory states in (1.1) "flow" to the energies of string theory states as the coupling increases.…”

Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory at Strong Coupling

“…In parallel development, the computation of the two-loop O(1/g) corrections to the string theory prediction (1) was initiated in [19]. Also, the result (1) was reproduced [20] from the quantum string Bethe ansatz for a folded string rotating in AdS 3 ×S 1 . In this Letter, we describe an approach to finding a strong coupling expansion of the solution to equation (2).…”

Embedding nonlinear sigma model into super-Yang–Mills theory

“…• For ξ ≫ 1 the minimal anomalous dimension grows logarithmically with N and it has the following scaling behavior both at weak and at strong coupling [1,11,13,2,14] …”