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Title: Bootstrapping the Three-Loop Hexagon

Abstract

We consider the hexagonal Wilson loop dual to the six-point MHV amplitude in planar N = 4 super Yang-Mills theory. We apply constraints from the operator product expansion in the near-collinear limit to the symbol of the remainder function at three loops. Using these constraints, and assuming a natural ansatz for the symbol's entries, we determine the symbol up to just two undetermined constants. In the multi-Regge limit, both constants drop out from the symbol, enabling us to make a non-trivial confirmation of the BFKL prediction for the leading-log approximation. This result provides a strong consistency check of both our ansatz for the symbol and the duality between Wilson loops and MHV amplitudes. Furthermore, we predict the form of the full three-loop remainder function in the multi-Regge limit, beyond the leading-log approximation, up to a few constants representing terms not detected by the symbol. Our results confirm an all-loop prediction for the real part of the remainder function in multi-Regge 3 {yields} 3 scattering. In the multi-Regge limit, our result for the remainder function can be expressed entirely in terms of classical polylogarithms. For generic six-point kinematics other functions are required.

Authors:
; ;
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1029137
Report Number(s):
SLAC-PUB-14528
Journal ID: ISSN 1029-8479; arXiv:1108.4461; TRN: US1105623
DOE Contract Number:  
AC02-76SF00515
Resource Type:
Journal Article
Journal Name:
JHEP 1111:023,2011
Additional Journal Information:
Journal Volume: 2011; Journal Issue: 11; Journal ID: ISSN 1029-8479
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AMPLITUDES; DUALITY; FORECASTING; OPERATOR PRODUCT EXPANSION; SCATTERING; SUPERSYMMETRY; SYMMETRY; WILSON LOOP; YANG-MILLS THEORY; Theory-HEP,HEPTH

Citation Formats

Dixon, Lance J, /CERN /SLAC, Drummond, James M, /CERN /Annecy, LAPTH, Henn, Johannes M, and /Humboldt U., Berlin /Santa Barbara, KITP. Bootstrapping the Three-Loop Hexagon. United States: N. p., 2011. Web. doi:10.1007/JHEP11(2011)023.
Dixon, Lance J, /CERN /SLAC, Drummond, James M, /CERN /Annecy, LAPTH, Henn, Johannes M, & /Humboldt U., Berlin /Santa Barbara, KITP. Bootstrapping the Three-Loop Hexagon. United States. doi:10.1007/JHEP11(2011)023.
Dixon, Lance J, /CERN /SLAC, Drummond, James M, /CERN /Annecy, LAPTH, Henn, Johannes M, and /Humboldt U., Berlin /Santa Barbara, KITP. Tue . "Bootstrapping the Three-Loop Hexagon". United States. doi:10.1007/JHEP11(2011)023. https://www.osti.gov/servlets/purl/1029137.
@article{osti_1029137,
title = {Bootstrapping the Three-Loop Hexagon},
author = {Dixon, Lance J and /CERN /SLAC and Drummond, James M and /CERN /Annecy, LAPTH and Henn, Johannes M and /Humboldt U., Berlin /Santa Barbara, KITP},
abstractNote = {We consider the hexagonal Wilson loop dual to the six-point MHV amplitude in planar N = 4 super Yang-Mills theory. We apply constraints from the operator product expansion in the near-collinear limit to the symbol of the remainder function at three loops. Using these constraints, and assuming a natural ansatz for the symbol's entries, we determine the symbol up to just two undetermined constants. In the multi-Regge limit, both constants drop out from the symbol, enabling us to make a non-trivial confirmation of the BFKL prediction for the leading-log approximation. This result provides a strong consistency check of both our ansatz for the symbol and the duality between Wilson loops and MHV amplitudes. Furthermore, we predict the form of the full three-loop remainder function in the multi-Regge limit, beyond the leading-log approximation, up to a few constants representing terms not detected by the symbol. Our results confirm an all-loop prediction for the real part of the remainder function in multi-Regge 3 {yields} 3 scattering. In the multi-Regge limit, our result for the remainder function can be expressed entirely in terms of classical polylogarithms. For generic six-point kinematics other functions are required.},
doi = {10.1007/JHEP11(2011)023},
journal = {JHEP 1111:023,2011},
issn = {1029-8479},
number = 11,
volume = 2011,
place = {United States},
year = {2011},
month = {11}
}