Dilogarithm ladders from Wilson loops

We consider a light-like Wilson loop in N = 4 SYM evaluated on a regular n-polygon contour. Sending the number of edges to infinity the polygon approximates a circle and the expectation value of the light-like WL is expected to tend to the localization result for the circular one. We show this expli...

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Detalles Bibliográficos
Autores principales:	Bianchi, M.S., Leoni, M.
Formato:	JOUR
Materias:	Scattering Amplitudes Wilson ’t Hooft and Polyakov loops
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_11266708_v2015_n2_p_Bianchi
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_11266708_v2015_n2_p_Bianchi
record_format	dspace
spelling	todo:paper_11266708_v2015_n2_p_Bianchi2023-10-03T16:07:19Z Dilogarithm ladders from Wilson loops Bianchi, M.S. Leoni, M. Scattering Amplitudes Wilson ’t Hooft and Polyakov loops We consider a light-like Wilson loop in N = 4 SYM evaluated on a regular n-polygon contour. Sending the number of edges to infinity the polygon approximates a circle and the expectation value of the light-like WL is expected to tend to the localization result for the circular one. We show this explicitly at one loop, providing a prescription to deal with the divergences of the light-like WL and the large n limit. Taking this limit entails evaluating certain sums of dilogarithms which, for a regular polygon, evaluate to the same constant independently of n. We show that this occurs thanks to underlying dilogarithm identities, related to the so-called “polylogarithm ladders”, which appear in rather different contexts of physics and mathematics and enable us to perform the large n limit analytically. © 2015, The Author(s). JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_11266708_v2015_n2_p_Bianchi
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Scattering Amplitudes Wilson ’t Hooft and Polyakov loops
spellingShingle	Scattering Amplitudes Wilson ’t Hooft and Polyakov loops Bianchi, M.S. Leoni, M. Dilogarithm ladders from Wilson loops
topic_facet	Scattering Amplitudes Wilson ’t Hooft and Polyakov loops
description	We consider a light-like Wilson loop in N = 4 SYM evaluated on a regular n-polygon contour. Sending the number of edges to infinity the polygon approximates a circle and the expectation value of the light-like WL is expected to tend to the localization result for the circular one. We show this explicitly at one loop, providing a prescription to deal with the divergences of the light-like WL and the large n limit. Taking this limit entails evaluating certain sums of dilogarithms which, for a regular polygon, evaluate to the same constant independently of n. We show that this occurs thanks to underlying dilogarithm identities, related to the so-called “polylogarithm ladders”, which appear in rather different contexts of physics and mathematics and enable us to perform the large n limit analytically. © 2015, The Author(s).
format	JOUR
author	Bianchi, M.S. Leoni, M.
author_facet	Bianchi, M.S. Leoni, M.
author_sort	Bianchi, M.S.
title	Dilogarithm ladders from Wilson loops
title_short	Dilogarithm ladders from Wilson loops
title_full	Dilogarithm ladders from Wilson loops
title_fullStr	Dilogarithm ladders from Wilson loops
title_full_unstemmed	Dilogarithm ladders from Wilson loops
title_sort	dilogarithm ladders from wilson loops
url	http://hdl.handle.net/20.500.12110/paper_11266708_v2015_n2_p_Bianchi
work_keys_str_mv	AT bianchims dilogarithmladdersfromwilsonloops AT leonim dilogarithmladdersfromwilsonloops
_version_	1807321999573254144

Dilogarithm ladders from Wilson loops

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