Superconformal symmetry and two-loop amplitudes in planar N = 4 super Yang-Mills

By S. Caron-Huot. 2011

184 citations recorded by the source corpus.

A bstractScattering amplitudes in superconformal field theories do not enjoy this symmetry, because the definition of asymptotic states involve a notion of infinity. Concentrating on planar $ \mathcal{N} = {4} $ Yang-Mills, we consider a generalization of scattering amplitudes which depends on twice as many Grassmann variables. We conjecture that it restores at least half of the superconformal symmetries, and all of the dual superconformal symmetries. The object arises naturally as the dual of a null polygonal Wilson loop in an ($ x,\;\theta, \;\overline \theta $) superspace. We support the conjecture by using it to obtain the total differential of all n-point two-loop MHV amplitudes, and showing that the result passes consistency checks. Potential all-loop constraints are also discussed.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/d4f7d775de20ce8177aa3cb2ee95a5474b4dcf2e

How researchers see this paper

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

In Astronomy and Astrophysics

1. N. Arkani-Hamed
2. L. Dixon
3. J. Trnka
4. F. Cachazo
5. J. Drummond
6. J. Bourjaily
7. M. Spradlin
8. A. Volovich

In Nuclear and High Energy Physics

1. L. Dixon
2. Claude Duhr
3. J. Drummond
4. M. Hippel
5. N. Arkani-Hamed
6. S. Caron-Huot
7. J. Henn
8. M. Spradlin

Citations in the corpus

• Space-time S-matrix and flux tube S-matrix II. Extracting and matching data (2013, background): “The latter is not known yet as a function but fortunately its symbol has already been found [11].”
• Scattering Amplitudes and the Positive Grassmannian (2012, background): “The symbol for all 2-loop MHV amplitudes has been determined, [21] (see”
• Bootstrapping the three-loop hexagon (2011, background): “[38], which suggests that this fact may be related to a supersymmetric formulation of the Wilson loop.”
• Motivic amplitudes and cluster coordinates (2013, methodology): “15), appear in the symbol of the two-loop n = 8 MHV amplitude [54], and the simpler ones of the type in eq.”
• From polygons and symbols to polylogarithmic functions (2011, background): “In practice, such tensors could come from computing a Feynman integral in terms of multiple polylogarithms, or by computing its symbol by other means [63, 64, 65, 67, 70, 73].”
• Heptagons from the Steinmann cluster bootstrap (2016, background): “The symbols of the two- and three-loop seven-point BDS remainder functions R (2) 7 , R (3) 7 are known [12, 79].”
• Hexagon functions and the three-loop remainder function (2013, background): “More importantly, the number of letters in the symbol grows quite rapidly, even at two loops [73], increasing the complexity of the problem.”
• A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon (2014, methodology): “For example, it is known [65] that the two-loop n-particle MHV remainder function is written in terms of a symbol alphabet of precisely 32n(n − 5) 2 (projectively invariant) letters.”
• 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,”