Magic identities for conformal four-point integrals

By J. Drummond, J. Henn, Vladimir A. Smirnov, E. Sokatchev. 2006

511 citations recorded by the source corpus.

We propose an iterative procedure for constructing classes of off-shell four-point conformal integrals which are identical. The proof of the identity is based on the conformal properties of a subintegral common for the whole class. The simplest example are the so-called `triple scalar box' and `tennis court' integrals. In this case we also give an independent proof using the method of Mellin–Barnes representation which can be applied in a similar way for general off-shell Feynman integrals.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/4b66948cde7de11a39182f993d809d6535f20f95

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In Astronomy and Astrophysics

1. N. Beisert
2. R. Roiban
3. A. Tseytlin
4. S. Frolov
5. S. Caron-Huot
6. J. Maldacena
7. N. Arkani-Hamed
8. J. Drummond

In Nuclear and High Energy Physics

1. S. Caron-Huot
2. L. Dixon
3. J. Drummond
4. J. Maldacena
5. L. Alday
6. R. Roiban
7. J. Henn
8. P. Vieira

Citations in the corpus

• From correlation functions to scattering amplitudes (2010, background): “Switching from momenta to dual coordinates [13], k = x1 − x0, l = x0′ − x1 and pi = xi − xi+1 (with x5 ≡ x1) , we identify the pseudo-conformal integrals from the correlator with those from the amplitude (see Fig.”
• Motivic amplitudes and cluster coordinates (2013, background): “A very special feature of SYM theory in the planar limit is that all amplitudes are invariant under conformal transformations in this dual space-time [14–21] It is often useful, especially when one is interested in discussing aspects of conformal symmetry, to compactify the space-time.”
• Scattering amplitudes, Wilson loops and the string/gauge theory correspondence (2008, background): “It was observed in [88] by explicitly inspecting the known results for the one-, two- and three-loop four-gluon amplitudes that the integrals appearing in the rescaled amplitude M4 exhibit, if regularized by keeping the external legs off-shell, (in a sense we will describe below) an SO(2, 4) symmetr”
• Scattering Amplitudes and the Positive Grassmannian (2012, background): “(Dual super-conformal invariance was first noticed in multi-loop perturbative calculations, [117], and then at strong coupling, [118]; this led to a remarkable connection between null-polygonal Wilson loops and scattering amplitudes—see e.”
• Single-valued harmonic polylogarithms and the multi-Regge limit (2012, background): “Remarkably, the planar N = 4 super-Yang-Mills amplitudes are governed by a dual conformal symmetry acting on the xi [1, 2, 3, 4, 5, 6, 7].”
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes (2007, unknown): “Secondly, the gluon amplitudes have the intriguing property of ‘dual’ conformal symmetry [14].”
• Notes on the scattering amplitude — Wilson loop duality (2010, background): “Further evidence for this hidden symmetry accumulated in the course of higher-loop computations, where it was repeatedly found that all integrals appearing in loop corrections shared this property [5, 6].”
• A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon (2014, background): “The duality with Wilson loops [3, 4, 5, 6, 7, 8, 9] and the associated dual conformal symmetry [7, 10, 11, 12, 13] of the planar theory mean that only amplitudes with six or more external legs are non-trivial.”
• Bootstrapping an NMHV amplitude through three loops (2014, background): “In addition, empirical results have led to the discovery of many hidden properties of planar N = 4 SYM, such as dual (super)conformal invariance [8–12], and the amplitude-Wilson-loop duality [11, 13–16].”
• On planar gluon amplitudes/Wilson loops duality (2007, background): “These integrals were shown to be conformal up to three loops in [23] by writing the momenta in terms of dual coordinates.”
• Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection (2008, background): “We have not been very explicit about the precise form of the vertex operators, but it seems clear that the symmetries are such that one should reproduce the structure described in [13] (and also [12]).”