Hexagonal Wilson loop with Lagrangian insertion at two loops in N $$ \mathcal{N} $$ = 4 super Yang-Mills theory

Abstract In this work, we compute the two-loop result of the null hexagonal Wilson loop with a Lagrangian insertion in planar, maximally supersymmetric Yang-Mills theory via a bootstrap approach. Normalized by the null polygonal Wilson loop itself, the integrand-level result of this observable corre...

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Main Authors: Sérgio Carrôlo, Dmitry Chicherin, Johannes Henn, Qinglin Yang, Yang Zhang
Format: Article
Language:English
Published: SpringerOpen 2025-07-01
Series:Journal of High Energy Physics
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Online Access:https://doi.org/10.1007/JHEP07(2025)214
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author Sérgio Carrôlo
Dmitry Chicherin
Johannes Henn
Qinglin Yang
Yang Zhang
author_facet Sérgio Carrôlo
Dmitry Chicherin
Johannes Henn
Qinglin Yang
Yang Zhang
author_sort Sérgio Carrôlo
collection DOAJ
description Abstract In this work, we compute the two-loop result of the null hexagonal Wilson loop with a Lagrangian insertion in planar, maximally supersymmetric Yang-Mills theory via a bootstrap approach. Normalized by the null polygonal Wilson loop itself, the integrand-level result of this observable corresponds to the logarithm of the six-point three-loop amplitude in this theory, while its integrated result is conjectured to match the maximally transcendental part of the six-point three-loop all-plus amplitude in pure Yang-Mills theory. Our work builds on two recent advances. On the one hand, the set of leading singularities relevant to this observable was recently classified. On the other hand, the relevant space of special functions that may in principle accompany these leading singularities was determined at two loops and for six particles by a dedicated Feynman integral calculation. These two ingredients serve as the foundation of our bootstrap ansatz. We fix all indeterminates in this ansatz by imposing physical constraints, such as symmetries, absence of spurious divergences, and correct behavior in soft and collinear limits. Finally, we discuss and verify certain physical properties of our symbol result, including physical singularities, behavior under multi-Regge limit, as well as Steinmann relations between symbol entries. The latter relations are motivated by the correspondence to all-plus amplitudes in pure Yang-Mills theory, and successfully checking them constitutes a consistency check of this conjectured correspondence.
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series Journal of High Energy Physics
spelling doaj-art-19121123c160429b8f5b46f091319c542025-08-20T03:42:22ZengSpringerOpenJournal of High Energy Physics1029-84792025-07-012025713110.1007/JHEP07(2025)214Hexagonal Wilson loop with Lagrangian insertion at two loops in N $$ \mathcal{N} $$ = 4 super Yang-Mills theorySérgio Carrôlo0Dmitry Chicherin1Johannes Henn2Qinglin Yang3Yang Zhang4Max-Planck-Institut für Physik, Werner-Heisenberg-InstitutLAPTh, Université Savoie Mont Blanc, CNRSMax-Planck-Institut für Physik, Werner-Heisenberg-InstitutMax-Planck-Institut für Physik, Werner-Heisenberg-InstitutInterdisciplinary Center for Theoretical Study, University of Science and Technology of ChinaAbstract In this work, we compute the two-loop result of the null hexagonal Wilson loop with a Lagrangian insertion in planar, maximally supersymmetric Yang-Mills theory via a bootstrap approach. Normalized by the null polygonal Wilson loop itself, the integrand-level result of this observable corresponds to the logarithm of the six-point three-loop amplitude in this theory, while its integrated result is conjectured to match the maximally transcendental part of the six-point three-loop all-plus amplitude in pure Yang-Mills theory. Our work builds on two recent advances. On the one hand, the set of leading singularities relevant to this observable was recently classified. On the other hand, the relevant space of special functions that may in principle accompany these leading singularities was determined at two loops and for six particles by a dedicated Feynman integral calculation. These two ingredients serve as the foundation of our bootstrap ansatz. We fix all indeterminates in this ansatz by imposing physical constraints, such as symmetries, absence of spurious divergences, and correct behavior in soft and collinear limits. Finally, we discuss and verify certain physical properties of our symbol result, including physical singularities, behavior under multi-Regge limit, as well as Steinmann relations between symbol entries. The latter relations are motivated by the correspondence to all-plus amplitudes in pure Yang-Mills theory, and successfully checking them constitutes a consistency check of this conjectured correspondence.https://doi.org/10.1007/JHEP07(2025)214Scattering AmplitudesSupersymmetric Gauge TheoryWilson’t Hooft and Polyakov loopsAdS-CFT Correspondence
spellingShingle Sérgio Carrôlo
Dmitry Chicherin
Johannes Henn
Qinglin Yang
Yang Zhang
Hexagonal Wilson loop with Lagrangian insertion at two loops in N $$ \mathcal{N} $$ = 4 super Yang-Mills theory
Journal of High Energy Physics
Scattering Amplitudes
Supersymmetric Gauge Theory
Wilson
’t Hooft and Polyakov loops
AdS-CFT Correspondence
title Hexagonal Wilson loop with Lagrangian insertion at two loops in N $$ \mathcal{N} $$ = 4 super Yang-Mills theory
title_full Hexagonal Wilson loop with Lagrangian insertion at two loops in N $$ \mathcal{N} $$ = 4 super Yang-Mills theory
title_fullStr Hexagonal Wilson loop with Lagrangian insertion at two loops in N $$ \mathcal{N} $$ = 4 super Yang-Mills theory
title_full_unstemmed Hexagonal Wilson loop with Lagrangian insertion at two loops in N $$ \mathcal{N} $$ = 4 super Yang-Mills theory
title_short Hexagonal Wilson loop with Lagrangian insertion at two loops in N $$ \mathcal{N} $$ = 4 super Yang-Mills theory
title_sort hexagonal wilson loop with lagrangian insertion at two loops in n mathcal n 4 super yang mills theory
topic Scattering Amplitudes
Supersymmetric Gauge Theory
Wilson
’t Hooft and Polyakov loops
AdS-CFT Correspondence
url https://doi.org/10.1007/JHEP07(2025)214
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