Cluster adjacency and the four-loop NMHV heptagon

We study the maximally-helicity-violating (MHV) six-gluon scattering amplitude in planar N = 4 super-Yang-Mills theory at finite coupling when all three cross ratios are small. It exhibits a double logarithmic scaling in the cross ratios, controlled by a handful of "anomalous dimensions" that are functions of the coupling constant alone. Inspired by known seven-loop results at weak coupling and the integrability-based pentagon OPE, we present conjectures for the all-order resummation of these anomalous dimensions. At strong coupling, our predictions agree perfectly with the string theory analysis. Intriguingly, the simplest of these anomalous dimensions coincides with one describing the light-like limit of the octagon, namely the four-point function of large-charge BPS operators. arXiv:2001.05460v1 [hep-th]

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“…where ξ is a vector of variables conjugate to the charges (16) and where N is the normalization factor,…”

Section: A Secretly Gaussian Integralmentioning

confidence: 99%

“…Powerful bootstrap techniques [8][9][10][11][12] allow the construction of the six-gluon maximally-helicity-violating (MHV) amplitude through seven loops, and the next-to-MHV amplitude through six loops [13]. Seven-point amplitudes have also been bootstrapped through four loops [14][15][16] at the level of the symbol [17].…”

Section: Introductionmentioning

confidence: 99%

Origin of the Six-Gluon Amplitude in Planar N=4 Supersymmetric Yang-Mills Theory

2020

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“…In cyclic sum, however, all these additional letters cancel-and quite nontrivially. For example, among these contributions only the entire cyclic sum of I 2 +I 3 +I 4 +I 5 is free of 'spurious' letters relative to the 42 letter alphabet expected for heptagon functions [69] (see also [47][48][49][91][92][93][94][95]). For the sake of those readers interested in more details, we have provided the additional symbol letters that arise for the cyclic seed integrals in the ancillary files to this work.…”

Section: Symbology and The Alphabets Of Individual Integral Contributmentioning

confidence: 99%

“…Today, this particular quantity-the six-particle remainder function in planar sYM-is known to seven(!) loops; and the seven-particle remainder is known (at least at 'symbol-level') to four loops [38][39][40][41][42][43][44][45][46][47][48][49]. Interestingly, after the two-loop result was found 'the old fashioned way' in [36]-namely, by integrating Feynman integrands-all subsequent results were obtained using methods that made no reference to loop integrands or loop integration whatsoever !…”

Section: Introduction and Overviewmentioning

confidence: 99%

Conformally-regulated direct integration of the two-loop heptagon remainder

Bourjaily

Volk

Hippel

2020

J. High Energ. Phys.

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We reproduce the two-loop seven-point remainder function in planar, maximally supersymmetric Yang-Mills theory by direct integration of conformallyregulated chiral integrands. The remainder function is obtained as part of the twoloop logarithm of the MHV amplitude, the regularized form of which we compute directly in this scheme. We compare the scheme-dependent anomalous dimensions and related quantities in the conformal regulator with those found for the Higgs regulator.

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“…refs. [25][26][27][28][29][30][31][32][33][34][35][36]). This property is commonly referred to as maximal transcendentality [37,38], and the maximally supersymmetric theory has thus far remained unique in this regard among Yang-Mills theories.…”

Section: Introductionmentioning

confidence: 99%

Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes

Kälin

Mogull

Ochirov

et al. 2020

J. High Energ. Phys.

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Using a careful choice of infrared (IR) subtraction scheme, we demonstrate the cancellation of all terms with transcendental weights 0,1,2 from the finite part of the full-color two-loop four-gluon N = 2 supersymmetric QCD amplitude, with N f massless supersymmetric quarks. This generalizes the previously observed cancellation of weight-2 terms in the superconformal theory, where N f = 2N c for gauge group SU(N c ). The subtraction scheme follows naturally both from general IR factorization principles and from an integrand-level analysis of divergences in this amplitude. The divergences are written in terms of scalar triangle integrals whose expressions are known to all orders in the dimensional regulator = (4 − D)/2. We also present integrated expressions for the full-color two-loop four-point amplitudes with both matter and vectors on external legs in which lower-weight terms also cancel using an appropriate IR scheme. This provides us with values for the two-loop cusp, gluonic, and quark anomalous dimensions in N = 2 supersymmetric QCD, which are cross-checked between the three different amplitudes.

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Cluster adjacency and the four-loop NMHV heptagon

Cited by 99 publications

References 59 publications

Origin of the Six-Gluon Amplitude in Planar N=4 Supersymmetric Yang-Mills Theory

Origin of the Six-Gluon Amplitude in Planar N=4 Supersymmetric Yang-Mills Theory

Conformally-regulated direct integration of the two-loop heptagon remainder

Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes

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