Pulling the straps of polygons

By D. Gaiotto, J. Maldacena, A. Sever, P. Vieira. 2011

208 citations recorded by the source corpus.

A bstractUsing the Operator Product Expansion for Wilson loops we derive a simple formula giving the discontinuities of the two loop result in terms of the one loop answer. We also argue that the knowledge of these discontinuities should be enough to fix the full two loop answer, for a general number of sides. We work this out explicitly for the case of the hexagon and rederive the known result.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/566b67d214013b00e56fba477607d6a383f88b2d

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Theoretical Computer Science

Citations in the corpus

Motivic amplitudes and cluster coordinates (2013, background): “Also, it has long been appreciated that the behavior of amplitudes under collinear (and especially multi-collinear) limits strongly constrains their structure, and the operator product expansion (OPE) to the null polygonal Wilson loop [75–78] aims to compute arbitrary amplitudes at finite coupling i”
Space-time S-matrix and flux tube S-matrix II. Extracting and matching data (2013, background): “The bound-state family comprise the two towers D z Fz− and D m z̄ Fz̄− which played an important role in previous OPE analysis [1, 24].”
Heptagons from the Steinmann cluster bootstrap (2016, background): “A further constraint on the relevant space of functions comes from the restriction that only physical branch cuts can appear in the remainder and ratio functions [41].”
Bootstrapping an NMHV amplitude through three loops (2014, background): “Thanks to the equivalence between amplitudes and polygonal Wilson loops, this limit corresponds to an operator product expansion (OPE) [36–39].”
Single-valued harmonic polylogarithms and the multi-Regge limit (2012, background): “6) The first entry of the symbol is actually restricted to the set {u1, u2, u3} due to the location of the amplitude’s branch cuts [27]; the integrability of the symbol restricts the second entry to the set {ui, 1− ui} [27, 28]; and a “final-entry condition” [28, 34] implies that there are only six,”
Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes (2012, background): “Since their introduction, symbols have seen many applications in physics [44, 45, 46, 47, 48, 49, 50, 51, 52, 53].”
Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions (2014, methodology): “The relevant analysis was carried out in [17] (see also [18] and [19]) building on previous studies [20, 21].”
From polygons and symbols to polylogarithmic functions (2011, methodology): “case an integrated form of the symbol is also known. Other approaches, aiming at the determination of the symbol of loop amplitudes by exploiting the operator product expansion in the collinear limit [66, 67] or the relationship between Feynman integrals and the volumes of polyhedra in non-euclidean”
The four-loop six-gluon NMHV ratio function (2015, background): “Their branch cuts are only in u, v and w, and not in any of the other six symbol letters [55].”
Bootstrapping the three-loop hexagon (2011, methodology): “[41] we can say that it must obey certain differential equations.”
Superconformal symmetry and two-loop amplitudes in planar N = 4 super Yang-Mills (2011, methodology): “This is quite similar to the pairing of two Wilson loops in [15], except now we have two edges in AdS.”
Hexagon functions and the three-loop remainder function (2013, background): “The initial entries in the symbol can only be the cross ratios themselves, in order to have physical branch cuts [17]:”
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”
Mathematical aspects of scattering amplitudes (2014, background): “In particular, for massless propagators this implies that the first entry in the symbol of such an integral can only be a Mandelstam invariant [36].”