Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
By Z. Bern, J. J. Carrasco, H. Johansson, David A. Kosower. 2007
272 citations recorded by the source corpus.
We present an Ansatz for the planar five-loop four-point amplitude in maximally supersymmetric Yang-Mills theory in terms of loop integrals. This Ansatz exploits the recently observed correspondence between integrals with simple conformal properties and those found in the four-point amplitudes of the theory through four loops. We explain how to identify all such integrals systematically. We make use of generalized unitarity in both four and D dimensions to determine the coefficients of each of these integrals in the amplitude. Maximal cuts, in which we cut all propagators of a given integral, are an especially effective means for determining these coefficients. The set of integrals and coefficients determined here will be useful for computing the five-loop cusp anomalous dimension of the theory which is of interest for nontrivial checks of the AdS/CFT duality conjecture. It will also be useful for checking a conjecture that the amplitudes have an iterative structure allowing for their all-loop resummation, whose link to a recent string-side computation by Alday and Maldacena opens a new venue for quantitative AdS/CFT comparisons.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/031deddf909996ccddd30649177d4557025f2f45
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In Nuclear and High Energy Physics
Citations in the corpus
- A two-loop five-gluon helicity amplitude in QCD (2013, unknown): “1 The pentagon-box: (431) The maximum eight-fold cut can be parametrized using three free parameters τ1, τ2 and τ3, as k̄ 1 = a1p μ 1 + a2p μ 2 + a3 〈23〉 2〈13〉〈1|γμ|2] + a4 [23] 2[13]〈2|γμ|1], k̄ 2 = b1p μ 4 + b2p μ 5 + b3 〈51〉 2〈41〉〈4|γμ|5] + b4 [51] 2[41]〈5|γμ|4], (3.”
- Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes (2007, unknown): “The encouraging fact is that the n = 4 gluon amplitudes have been shown to possess a peculiar ‘hidden’ or ‘dual’ conformal symmetry [25] (different from the conformal symmetry of the underlying N = 4 theory) up to four loops [26] (and even at five loops [27]).”
- Hexagon Wilson loop = six-gluon MHV amplitude (2008, unknown): “…such pseudo-conformal integrals (for example, all the integrals in the four-gluon amplitude up to four (five) loops appear with coefficients ± 1 [39, 50, 17, 52]). the The exact link between the pseudo-conformal property of the integrals and dual conformal behavior of the amplitude is still unclear.”
- The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM (2010, methodology): “Complete integrands have been computed at twoloop order for 5-particles in [15] using D-dimensional unitarity and for 5- and 6-particles in [55,57] using the leading singularity technique developed in [57, 58].”
- Bootstrapping an NMHV amplitude through three loops (2014, background): “Many of the more powerful approaches toN = 4 supersymmetric scattering amplitudes compute the loop integrand of the theory [1–3, 5, 9, 10, 17–20].”
- Two-loop integrand decomposition into master integrals and surface terms (2015, background): “thermore, in analogy to the numerical one-loop unitarity approach, the integral coefficients can be computed through generalized unitarity cuts [45] by solving linear equations (e.”