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 in | The journal of high energy physics Vol. 2020; no. 10; pp. 1 - 45 |
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| Language | English |
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06.10.2020
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| Abstract | 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. |
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| AbstractList | 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. Seven-point amplitudes in planar $ \mathcal{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. In this work, 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. 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. Abstract Seven-point amplitudes in planar N $$ \mathcal{N} $$ = 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. |
| ArticleNumber | 31 |
| Author | Liu, Yu-Ting Dixon, Lance J. |
| Author_xml | – sequence: 1 givenname: Lance J. orcidid: 0000-0003-4985-7518 surname: Dixon fullname: Dixon, Lance J. organization: SLAC National Accelerator Laboratory, Stanford University – sequence: 2 givenname: Yu-Ting orcidid: 0000-0003-1978-9200 surname: Liu fullname: Liu, Yu-Ting email: aytliu@stanford.edu organization: SLAC National Accelerator Laboratory, Stanford University |
| BackLink | https://www.osti.gov/servlets/purl/1769109$$D View this record in Osti.gov |
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bstract
Seven-point amplitudes in planar
N
= 4 super-Yang-Mills theory have previously been constructed through four loops using the Steinmann cluster... Seven-point amplitudes in planar $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory have previously been constructed through four loops using the Steinmann... Seven-point amplitudes in planar $ \mathcal{N} $ = 4 super-Yang-Mills theory have previously been constructed through four loops using the Steinmann cluster... Abstract Seven-point amplitudes in planar N $$ \mathcal{N} $$ = 4 super-Yang-Mills theory have previously been constructed through four loops using the... |
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| SubjectTerms | 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 |
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| Title | Lifting heptagon symbols to functions |
| URI | https://link.springer.com/article/10.1007/JHEP10(2020)031 https://www.osti.gov/servlets/purl/1769109 https://doaj.org/article/3b3e9eecca0e411cbe71be0312d34a91 |
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