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Combinatorics of the geometry of Wilson loop diagrams I: equivalence classes via matroids and polytopes

Part of: Quantum field theory; related classical field theories

Published online by Cambridge University Press:  26 February 2021

Susama Agarwala ,
Siân Fryer  and
Karen Yeats
Susama Agarwala*
Affiliation:
Johns Hopkins Applied Physics Lab, Laurel, MD, USA
Siân Fryer
Affiliation:
UC Santa Barbara, Santa Barbara, CA93106, USA e-mail: fryer@math.ucsb.edu
Karen Yeats
Affiliation:
Combinatorics and Optimization, University of Waterloo, Waterloo, ON, Canada e-mail: kayeats@uwaterloo.ca
*
e-mail: susama@alum.mit.edu
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Abstract

Wilson loop diagrams are an important tool in studying scattering amplitudes of SYM $N=4$ theory and are known by previous work to be associated to positroids. We characterize the conditions under which two Wilson loop diagrams give the same positroid, prove that an important subclass of subdiagrams (exact subdiagrams) corresponds to uniform matroids, and enumerate the number of different Wilson loop diagrams that correspond to each positroid cell. We also give a correspondence between those positroids which can arise from Wilson loop diagrams and directions in associahedra.

Keywords

Wilson loop diagramsNkMHV diagramspositroidsN = 4 SYM theory

MSC classification

Primary: 81T60: Supersymmetric field theories
Type
Article
Information
Canadian Journal of Mathematics , Volume 74 , Issue 4 , August 2022 , pp. 1177 - 1208
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Copyright
© Canadian Mathematical Society 2021

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Footnotes

SA was partially supported by an Office of Naval Research grant. KY is supported by an NSERC Discovery grant, by the Canada Research Chair program, and also, over some of the time this work was developed, by a Humboldt Fellowship from the Alexander von Humboldt foundation.

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