Virtual scaling function of AdS/CFT

Abstract

We write an integral equation that incorporates finite corrections to the large spin asymptotics of N ¼ 4 supersymmetric Yang-Mills theory twist operators from the nonlinear integral equation. We show that these corrections are an all-loop result, not affected by wrapping effects, and agree, after determining the strong coupling expansion, with string theory predictions.

Spiky strings in the SL(2) Bethe Ansatz at strong coupling from AdS/CFT

“…For n = 2 we recover the result for the folded string [12], this result is in full agreement with the one-loop computation from string theory [14,26]. For arbitrary n (5.20) is expected to be in agreement with the one-loop result computed from the sigma model [27].…”

“…We note that the integral equation is very similar to the equation in [12] and the solution can consequently be written as…”

“…where B 2 (g) denotes the virtual scaling function of twist 2 operators obtained in [12]. The leading large S term, i.e.…”

“…The subleading corrections for the ground state were computed in [11,12] using a method different than what will be convenient here. We will here use the same method as in [3,24] but also include subleading corrections, for convenience we include the corresponding computation for the ground state in appendix B.…”

“…Computations of quantum corrections to the folded string solution [4] at leading order in large S as well as its generalization to AdS 3 × S 1 [5][6][7] were recently used to successfully check such all loop asymptotic Bethe ansatz [8][9][10][11]. The all loop asymptotic Bethe ansatz computation was then extended to the subleading orders in large S expansion [11][12][13] and precise matching with the corresponding string theory computations [14] was found.…”