An operator product expansion for polygonal null Wilson loops

By L. Alday, D. Gaiotto, J. Maldacena, A. Sever, P. Vieira. 2010

278 citations recorded by the source corpus.

We consider polygonal Wilson loops with null edges in conformal gauge theories. We derive an OPE-like expansion when several successive lines of the polygon are becoming aligned. The limit corresponds to a collinear, or multicollinear, limit and we explain the systematics of all the subleading corrections, going beyond the leading terms that were previously considered. These subleading corrections are governed by excitations of high spin operators, or excitations of a flux tube that goes between two Wilson lines. The discussion is valid for any conformal gauge theory, for any coupling and in any dimension.For $ \mathcal{N} = 4 $ super Yang Mills we check this expansion at strong coupling and at two loops at weak coupling. We also make predictions for the remainder function at higher loops.In the process, we also derived a new version for the TBA integral equations that determine the strong coupling answer and present the area as the associated Yang-Yang functional.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/31d145402eefc0f63fdb8649c13d68d989ca8887

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. S. Caron-Huot
2. P. Vieira
3. Tim Adamo
4. A. Sever
5. D. Gaiotto
6. L. Dixon
7. J. Maldacena
8. B. Basso

In Nuclear and High Energy Physics

1. S. Caron-Huot
2. L. Dixon
3. J. Maldacena
4. J. Drummond
5. L. Alday
6. A. Sever
7. P. Vieira
8. M. Hippel

Citations in the corpus

• Superconformal symmetry and two-loop amplitudes in planar N = 4 super Yang-Mills (2011, methodology): “Arguably, it still remains elusive at weak coupling, despite at best some glimpses at it through the OPE approach to computing Wilson loops [13–15].”
• A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon (2014, background): “Moreover, the relation to Wilson loops means that the remainder function must obey constraints on its discontinuities [26, 27, 28, 29] and on the power-suppressed corrections [30, 31, 32, 33, 34, 35, 36] in the collinear limit coming from an operator product expansion”
• Bootstrapping the three-loop hexagon (2011, background): “Another important property of polygonal Wilson loops is that they should respect a particular operator product expansion (OPE) in the region where several consecutive edges are nearly collinear [39, 40].”
• Scattering amplitudes and Wilson loops in twistor space (2011, background): “We will frequently abbreviate δ̄0|4(Z1, Z2, Z3, Z4, Z5) by [1, 2, 3, 4, 5].”
• Form factors at strong coupling via a Y-system (2010, methodology): “The final area is given by the critical value of Yang-Yang functional [ 8 ].”
• Classical polylogarithms for amplitudes and Wilson loops. (2010, background): “recently studied in [22], will tightly constrain the general form of R (L) n .”
• Integrable Wilson loops (2012, background): “This spectrum is a crucial ingredient in the OPE approach to lightlike Wilson loops as discussed in [74, 75] and should be closely related to the excitation spectrum of the spinning string as studied in [76] (see also [77]).”
• From correlation functions to Wilson loops (2010, background): “1 of [39], where the large spin limit of single trace operators was considered.”
• Space-time S-matrix and flux tube S-matrix II. Extracting and matching data (2013, methodology): “For example, to extract the Hexagon one-loop ratio function using this package we simply define the Zs to be given by the hexagon twistors (156), run the command evaluate@superComponent[{1},{},{2},{3},{},{4}]@ratioIntegral[6,1] and finally Series expand the result.”
• Wall-crossing in coupled 2d-4d systems (2011, methodology): “Recently the methods of [1, 2] have found some surprising applications to scattering in N = 4 super Yang-Mills theory [82, 83, 84, 85].”
• Pulling the straps of polygons (2011, methodology): “The reason is that it corresponds to essentially zero momentum modes of the particle that has no anomalous dimension at zero momentum (as explained in [2] these can be viewed as Goldstone modes of some generators in SL(2)τ ).”
• Holographic three-point functions of semiclassical states (2010, background): “utions with non-zero angular momenta in AdS approach the boundary at a point only if the worldsheet is Minkowskian [8]. If the worldsheet is Euclidean, its boundary maps to a line in the target space [17, 9]. 4More precisely, they should be conjugate. 2 2 Holographic OPE One of the operators in the ”
• When does the gluon reggeize? (2013, background): “[88], and at weak coupling we must have R → 1 + O(|w| 1 2 ) where β controls the gap in the operator spectrum and is of order a at weak coupling.”
• Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions (2014, methodology): “In the planarN = 4 Super-Yang-Mills theory, null polygonal Wilson loops can be computed at any value of the coupling using the Operator Product Expansion [1].”
• Single-valued harmonic polylogarithms and the multi-Regge limit (2012, background): “A powerful constraint on the structure of the remainder function at higher loop order is provided by the operator product expansion (OPE) for polygonal Wilson loops [25, 26, 27].”