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Multi-Regge kinematics and the moduli space of Riemann spheres with marked points

Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
We show that scattering amplitudes in planar N = 4 Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes' theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L + 4 external legs. We also investigate non-MHV amplitudes, and we show that they can be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. Finally, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.
scattering amplitudes, super yang-mills, multi-regge kinematics
1029-8479
Duca, Vittorio Del
d54ca66c-517b-47ea-babd-260c74469325
Druc, Stefan
58fc55ea-32cb-41f9-8aed-b71326eaf2cc
Drummond, James
3ea15544-457f-4e72-8ad0-60f3136841db
Duhr, Claude
7bb86906-9c06-4901-8a48-9016ed3a8c6e
Dulat, Falko
563feaa9-21a6-4715-a9a3-bdaa507611bd
Marzucca, Robin
f86eb135-2beb-4bb9-9c0b-8e38bd8db8d6
Papathanasiou, Georgios
92cb6f58-cc1c-4166-8595-70b13c9ea734
Verbeek, Bram
e7632b00-f273-4278-b8da-e501c689ff62
Duca, Vittorio Del
d54ca66c-517b-47ea-babd-260c74469325
Druc, Stefan
58fc55ea-32cb-41f9-8aed-b71326eaf2cc
Drummond, James
3ea15544-457f-4e72-8ad0-60f3136841db
Duhr, Claude
7bb86906-9c06-4901-8a48-9016ed3a8c6e
Dulat, Falko
563feaa9-21a6-4715-a9a3-bdaa507611bd
Marzucca, Robin
f86eb135-2beb-4bb9-9c0b-8e38bd8db8d6
Papathanasiou, Georgios
92cb6f58-cc1c-4166-8595-70b13c9ea734
Verbeek, Bram
e7632b00-f273-4278-b8da-e501c689ff62

Duca, Vittorio Del, Druc, Stefan, Drummond, James, Duhr, Claude, Dulat, Falko, Marzucca, Robin, Papathanasiou, Georgios and Verbeek, Bram (2016) Multi-Regge kinematics and the moduli space of Riemann spheres with marked points. Journal of High Energy Physics. (doi:10.1007/JHEP08(2016)152).

Record type: Article

Abstract

We show that scattering amplitudes in planar N = 4 Super Yang-Mills in multi-Regge kinematics can naturally be expressed in terms of single-valued iterated integrals on the moduli space of Riemann spheres with marked points. As a consequence, scattering amplitudes in this limit can be expressed as convolutions that can easily be computed using Stokes' theorem. We apply this framework to MHV amplitudes to leading-logarithmic accuracy (LLA), and we prove that at L loops all MHV amplitudes are determined by amplitudes with up to L + 4 external legs. We also investigate non-MHV amplitudes, and we show that they can be obtained by convoluting the MHV results with a certain helicity flip kernel. We classify all leading singularities that appear at LLA in the Regge limit for arbitrary helicity configurations and any number of external legs. Finally, we use our new framework to obtain explicit analytic results at LLA for all MHV amplitudes up to five loops and all non-MHV amplitudes with up to eight external legs and four loops.

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More information

Accepted/In Press date: 28 June 2016
e-pub ahead of print date: 25 September 2016
Additional Information: 104 pages, six awesome figures and ancillary files containing the results in Mathematica format
Keywords: scattering amplitudes, super yang-mills, multi-regge kinematics
Organisations: Theory Group, Physics & Astronomy

Identifiers

Local EPrints ID: 409705
URI: http://eprints.soton.ac.uk/id/eprint/409705
ISSN: 1029-8479
PURE UUID: d14681db-8622-4fa8-907c-14184bb6b465

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Date deposited: 01 Jun 2017 04:06
Last modified: 21 Nov 2021 06:36

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Contributors

Author: Vittorio Del Duca
Author: Stefan Druc
Author: James Drummond
Author: Claude Duhr
Author: Falko Dulat
Author: Robin Marzucca
Author: Georgios Papathanasiou
Author: Bram Verbeek

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