A generalized scaling function for AdS/CFT

Freyhult, Lisa; Rej, Adam; Staudacher, Matthias

doi:10.1088/1742-5468/2008/07/p07015

Cited by 86 publications

(241 citation statements)

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“…Clearly, it would be interesting to explore the strong coupling expansions for other examples. Closely related examples are the generalized scaling function, proposed in [49], and the generalized cusp anomalous dimension (or equivalently the quark-antiquark potential), studied in [50][51][52][53][54]. As studied in [33,[55][56][57], the strong coupling analysis of the generalized scaling function is almost in parallel with the cusp anomalous dimension, and thus it is a good exercise to see its resurgent aspect along the line in this paper.…”

Section: Discussionmentioning

confidence: 82%

Resurgence of the cusp anomalous dimension

Dorigoni¹,

Hatsuda²

2015

J. High Energ. Phys.

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We revisit the strong coupling limit of the cusp anomalous dimension in planar N = 4 super Yang-Mills theory. It is known that the strong coupling expansion is asymptotic and non-Borel summable. As a consequence, the cusp anomalous dimension receives non-perturbative corrections, and the complete strong coupling expansion should be a resurgent transseries. We reveal that the perturbative and non-perturbative parts in the transseries are closely interrelated. Solving the Beisert-Eden-Staudacher equation systematically, we analyze in detail the large order behavior in the strong coupling perturbative expansion and show that the non-perturbative information is indeed encoded there. An ambiguity of (lateral) Borel resummations of the perturbative expansion is precisely canceled by the contributions from the non-perturbative sectors, and the final result is real and unambiguous.

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Section: Discussionmentioning

confidence: 82%

Resurgence of the cusp anomalous dimension

Dorigoni¹,

Hatsuda²

2015

J. High Energ. Phys.

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“…In fact, by describing the anomalous dimension through a non-linear integral equation [12] (like in other integrable theories [11]), it has been recently confirmed the Sudakov leading behaviour for s → +∞ [10,8] γ(g, s, L) = f (g, j) ln s + . .…”

Section: Introductionmentioning

confidence: 84%

The generalised scaling function: A note

2010

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A method for determining the generalised scaling function(s) arising in the high spin behaviour of long operator anomalous dimensions in the planar sl(2) sector of N = 4 SYM is proposed. The all-order perturbative expansion around the strong coupling is detailed for the prototypical third and fourth scaling functions, showing the emergence of the O(6) Non-Linear Sigma Model mass-gap from different SYM 'mass' functions. Remarkably, only the fourth one gains contribution from the non-BES reducible densities and also shows up, as first, NLSM interaction and specific model dependence. Finally, the computation of the n-th generalised function is sketched and might be easily finalised for checks versus the computations in the sigma model or the complete string theory. *

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“…An equation of exactly this form appears in ABJM [49], and, apart from the minus sign on the right hand side, it is the starting point for deriving the Eden-Staudacher [76], BeisertEden-Staudacher [62] and Freyhult-Rej-Staudacher [77] equations. However, these equations heavily rely on the exact form of the BES/BHL dressing phase [62,63], and there is no particular reason that the dressing phase in (4.7) should take the same form as the corresponding phases in N = 4 SYM and ABJM.…”

Section: Dualization Of the Full Bethe Equations?mentioning

confidence: 99%

Integrability, spin-chains and the AdS3/CFT2 correspondence

Sax

Stefański

2011

J. High Energ. Phys.

146

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Building on arXiv:0912.1723 [1], in this paper we investigate the AdS 3 /CFT 2 correspondence using integrability techniques. We present an all-loop Bethe Ansatz (BA) for strings on AdS 3 × S 3 × S 3 × S 1 , with symmetry d(2, 1; α) 2 , valid for all values of α. This construction relies on a novel, α-dependent generalisation of the Zhukovsky map. We investigate the weakly-coupled limit of this BA and of the all-loop BA for strings on AdS 3 × S 3 × T 4 . We construct integrable short-range spin-chains and Hamiltonians that correspond to these weakly-coupled BAs. The spin-chains are alternating and homogenous, respectively. The alternating spinchain can be regarded as giving some of the first hints about the unknown CFT 2 dual to string theory on AdS 3 ×S 3 ×S 3 ×S 1 . We show that, in the α → 1 limit, the integrable structure of the d(2, 1; α) 2 model is non-singular and keeps track of not just massive but also massless modes. This provides a way of incorporating massless modes into the integrability machinery of the AdS 3 /CFT 2 correspondence.

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A generalized scaling function for AdS/CFT

Cited by 86 publications

References 50 publications

Resurgence of the cusp anomalous dimension

Resurgence of the cusp anomalous dimension

The generalised scaling function: A note

Integrability, spin-chains and the AdS3/CFT2 correspondence

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