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

Bourjaily, Jacob L.; Volk, Matthias; Hippel, Matt von

doi:10.1007/jhep02(2020)095

Cited by 19 publications

(21 citation statements)

References 103 publications

(194 reference statements)

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“…On the other hand, the symbol information can be a very important computational springboard for computing the full function [21]. As full multiple polylogarithmic functions, the seven point amplitude is only known to two loops and only for the MHV amplitude [60][61][62], for which the symbol (actually the total differential) was found earlier [14].…”

Section: Jhep10(2020)031 Introductionmentioning

confidence: 99%

Lifting heptagon symbols to functions

Dixon

Liu

2020

J. High Energ. Phys.

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Seven-point amplitudes in planar $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory have previously been constructed through four loops using the Steinmann cluster bootstrap, but only at the level of the symbol. We promote these symbols to actual functions, by specifying their first derivatives and boundary conditions on a particular two-dimensional surface. To do this, we impose branch-cut conditions and construct the entire heptagon function space through weight six. We plot the amplitudes on a few lines in the bulk Euclidean region, and explore the properties of the heptagon function space under the coaction associated with multiple polylogarithms.

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Section: Jhep10(2020)031 Introductionmentioning

confidence: 99%

Lifting heptagon symbols to functions

Dixon

Liu

2020

J. High Energ. Phys.

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“…The first nontrivial amplitude at six points and two loops was obtained analytically by means of Feynman diagrams in simplified quasi-multi-Regge kinematics [46,47], which nevertheless provides the full answer in general kinematics due to the dual conformal symmetry of the theory [48,18,49,50]. Other formulations of the integrand of the theory are also amenable to direct integration [51]. In addition, apart from bootstrap "boundary data", theQ-equation [29] additionally provides alternative representations for amplitudes, as integrals over a collinear limit of amplitudes with higher multiplicity and MHV degree, and lower loop order.…”

Section: Introductionmentioning

confidence: 99%

The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes

Caron-Huot¹,

Dixon²,

Drummond³

et al. 2020

Proceedings of Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2019)

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We review the bootstrap method for constructing six-and seven-particle amplitudes in planar N = 4 super Yang-Mills theory, by exploiting their analytic structure. We focus on two recently discovered properties which greatly simplify this construction at symbol and function level, respectively: the extended Steinmann relations, or equivalently cluster adjacency, and the coaction principle. We then demonstrate their power in determining the six-particle amplitude through six and seven loops in the NMHV and MHV sectors respectively, as well as the symbol of the NMHV seven-particle amplitude to four loops.

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“…This point is dihedrally symmetric in n-particle kinematics. Drawing upon known representations for the two-loop six-and seven-particle remainder functions [70,71,94,138,139], we have evaluated R…”

Section: Numerical Results and Cross-checksmentioning

confidence: 99%

“…(2) 7 [70,71], after which we can similarly fix the constant in R Following [15], we parametrize the R…”

Section: Collinear Limitsmentioning

confidence: 99%

The two-loop remainder function for eight and nine particles

Golden

McLeod²

2021

J. High Energ. Phys.

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Two-loop MHV amplitudes in planar $$ \mathcal{N} $$ N = 4 supersymmetric Yang Mills theory are known to exhibit many intriguing forms of cluster-algebraic structure. We leverage this structure to upgrade the symbols of the eight- and nine-particle amplitudes to complete analytic functions. This is done by systematically projecting onto the components of these amplitudes that take different functional forms, and matching each component to an ansatz of multiple polylogarithms with negative cluster-coordinate arguments. The remaining additive constant can be determined analytically by comparing the collinear limit of each amplitude to known lower-multiplicity results. We also observe that the nonclassical part of each of these amplitudes admits a unique decomposition in terms of a specific A3 cluster polylogarithm, and explore the numerical behavior of the remainder function along lines in the positive region.

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

Cited by 19 publications

References 103 publications

Lifting heptagon symbols to functions

Lifting heptagon symbols to functions

The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes

The two-loop remainder function for eight and nine particles

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