Transcendentality and crossing

By N. Beisert, B. Eden, M. Staudacher. 2006

1,049 citations recorded by the source corpus.

We discuss possible phase factors for the S-matrix of planar gauge theory, leading to modifications at four-loop order as compared to an earlier proposal. While these result in a four-loop breakdown of perturbative BMN scaling, Kotikov–Lipatov transcendentality in the universal scaling function for large-spin twist operators may be preserved. One particularly natural choice, unique up to one constant, modifies the overall contribution of all terms containing odd-zeta functions in the earlier proposed scaling function based on a trivial phase. Excitingly, we present evidence that this choice is non-perturbatively related to a recently conjectured crossing-symmetric phase factor for perturbative string theory on AdS5 × S5 once the constant is fixed to a particular value. Our proposal, if true, might therefore resolve the long-standing AdS/CFT discrepancies between gauge and string theory.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/dad97433d02577418f25eb714d1548ea85e2fd93

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In Nuclear and High Energy Physics

1. S. Frolov
2. R. Roiban
3. A. Tseytlin
4. G. Arutyunov
5. L. Alday
6. N. Beisert
7. J. Maldacena
8. S. Caron-Huot

Citations in the corpus

• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes (2007, neutral): “We know that the former can be determined to all loops from a Bethe Ansatz [38, 39, 40] and its strong coupling limit matches the string theory prediction [41, 42, 8, 43].”
• The Bethe ansatz for superconformal Chern-Simons (2008, neutral): “∗Also at ITEP, Moscow, Russia”
• The Zamolodchikov-Faddeev Algebra for AdS5 x S5 Superstring (2006, background): “Thus, the ZF algebra provides an indispensable framework (1)It is still unclear if the proposal of [15] correctly describes bound states present in string and gauge theories at large values of the ’t Hooft coupling constant λ [20].”
• Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal (2008, methodology): “Being less than maximally supersymmetric, this new duality is useful as it reveals various seemingly obvious assumptions that were made (and eventually shown to be correct in the maximally supersymmetric context) in the construction of the solution for the spectrum of AdS/CFT4 based on the Bethe Ans”
• Hexagon functions and the three-loop remainder function (2013, background): “This relation holds for strong coupling as well as weak coupling, since the cusp anomalous dimension is known exactly [89].”
• The four-loop six-gluon NMHV ratio function (2015, background): “This quantity is known to all orders [93]; its expansion to four loops is given by”
• Four loop twist two, BFKL, wrapping and strings (2008, methodology): “the large spin (M) and twist (J) behaviour of their anomalous dimension ∆(M, J) is determined by the BES/FRS integral equations [10, 36].”
• Supersymmetric Wilson loops on S**3. (2007, result): “One particularly striking example are the recent results on the cusp anomalous dimension [4–9].”
• Integrable spin chain in superconformal Chern-Simons theory (2008, background): “Selected but nonexhaustive list of contributions in this subject include [5] - [21].”
• Dressing and wrapping (2007, background): “on the string side of the AdS/CFT correspondence, the asymptotic Bethe ansatz [9, 15]”
• Notes on superconformal Chern-Simons-Matter theories (2007, background): “(For a sample of recent advances see [5,6,7,8,9,10,11,12,13].”
• On the highest transcendentality in N=4 SUSY (2006, methodology): “Kr,s contributes to the perturbative results for the ES and BES equations (see [24, 23 ]), because ˆ Kr,s = Z ∞ 0 dz Jr(2gz)Js(2gz) z(ez − 1) (A16)”
• Erratum: On the structure of infrared singularities of gauge-theory amplitudes (2009, neutral): “Also, in [74, 75] an all-order form of the cusp anomalous dimension of planar N = 4 SYM was proposed, which is given by the solution of a certain integral equation.”
• The full four-loop cusp anomalous dimension in N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{do (2019, neutral): “The planar part of the cusp anomalous dimension is successfully described by integrability [29], with important input from perturbative calculations [77].”
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT (2006, methodology): “This would lead to many new checks of the proposed dressing phase [21, 18].”
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states (2008, background): “The specific form of the dressing factor is now believed to be known through a series of works [16, 17, 18, 19, 20, 21] and the first nontrivial coefficient at weak coupling was checked by a direct perturbative evaluation [22].”
• An operator product expansion for polygonal null Wilson loops (2010, background): “In N = 4 super Yang Mills one can compute these dimensions for all values of the coupling [8, 9].”
• Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions (2014, background): “The relevant analysis was carried out in [17] (see also [18] and [19]) building on previous studies [20, 21].”
• Foundations of the AdS5 × S5 superstring: I (2009, background): “An interesting proposal for the exact dressing factor has been put forward in [34].”