Lifting heptagon symbols to functions

A bstract Seven-point amplitudes in planar 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 co...

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Published inThe journal of high energy physics Vol. 2020; no. 10; pp. 1 - 45
Main Authors Dixon, Lance J., Liu, Yu-Ting
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 06.10.2020
Springer Berlin
SpringerOpen
Subjects
1/N Expansion
Classical and Quantum Gravitation
Elementary Particles
Physics
Physics and Astronomy
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Scattering Amplitudes
String Theory
Supersymmetric Gauge Theory
1
Scattering Amplitudes
Expansion
Supersymmetric Gauge Theory
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Summary:A bstract Seven-point amplitudes in planar 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.
Bibliography:USDOE Office of Science (SC), Basic Energy Sciences (BES)
AC02-76SF00515
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP10(2020)031