scholarly journals The three-loop MHV octagon from $$ \overline{Q} $$ equations

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Zhenjie Li ◽  
Chi Zhang
Keyword(s):  
Yang Mills ◽  
Remainder Function ◽  
Point Amplitude

Abstract The $$ \overline{Q} $$ Q ¯ equations, rooted in the dual superconformal anomalies, are a powerful tool for computing amplitudes in planar $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory. By using the $$ \overline{Q} $$ Q ¯ equations, we compute the symbol of the first MHV amplitude with algebraic letters — the three-loop 8-point amplitude (or the octagon remainder function) — in this theory. The symbol alphabet for this amplitude consists of 204 independent rational letters and shares the same 18 algebraic letters with the two-loop 8-point NMHV amplitude.

scholarly journals Complete four-loop four-point amplitude inN=4super-Yang-Mills theory

2010 ◽  
Vol 82 (12) ◽  
Author(s):  
Z. Bern ◽  
J. J. M. Carrasco ◽  
L. J. Dixon ◽  
H. Johansson ◽  
R. Roiban
Keyword(s):  
Yang Mills ◽  
Point Amplitude

scholarly journals Five-Loop Four-Point Amplitude ofN=4Super-Yang-Mills Theory

2012 ◽  
Vol 109 (24) ◽  
Author(s):  
Z. Bern ◽  
J. J. M. Carrasco ◽  
H. Johansson ◽  
R. Roiban
Keyword(s):  
Yang Mills ◽  
Point Amplitude

scholarly journals Exploring Reggeon bound states in strongly-coupled $$ \mathcal{N} $$ = 4 super Yang-Mills

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Theresa Abl ◽  
Martin Sprenger
Keyword(s):  
Analytic Continuation ◽  
Bound States ◽  
Large Mass ◽  
Bound State ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Remainder Function ◽  
Regge Limit ◽  
Case Basis ◽  
Number Of Particles

Abstract The multi-Regge limit of scattering amplitudes in strongly-coupled $$ \mathcal{N} $$ N = 4 super Yang-Mills is described by the large mass limit of a set of thermodynamic Bethe ansatz (TBA) equations. A non-trivial remainder function arises in this setup in certain kinematical regions due to excitations of the TBA equations which appear during the analytic continuation into these kinematical regions. So far, these analytic continuations were carried out on a case-by-case basis for the six- and seven-gluon remainder function. In this note, we show that the set of possible excitations appearing in any analytic continuation in the multi-Regge limit for any number of particles is rather constrained. In particular, we show that the BFKL eigenvalue of any possible Reggeon bound state is a multiple of the two-Reggeon BFKL eigenvalue appearing in the six-gluon case.

scholarly journals Evaluating the six-point remainder function near the collinear limit

2014 ◽  
Vol 29 (27) ◽  
pp. 1450154 ◽  
Author(s):  
Georgios Papathanasiou
Keyword(s):  
Scattering Amplitudes ◽  
High Energy Phys ◽  
Bound State ◽  
High Energy ◽  
Recent Proposal ◽  
Computational Tools ◽  
Yang Mills ◽  
Remainder Function ◽  
Leading Term ◽  
Collinear Limit

The simplicity of maximally supersymmetric Yang–Mills theory makes it an ideal theoretical laboratory for developing computational tools, which eventually find their way to QCD applications. In this contribution, we continue the investigation of a recent proposal by Basso, Sever and Vieira, for the nonperturbative description of its planar scattering amplitudes, as an expansion around collinear kinematics. The method of G. Papathanasiou, J. High Energy Phys.1311, 150 (2013), arXiv:1310.5735, for computing the integrals the latter proposal predicts for the leading term in the expansion of the six-point remainder function, is extended to one of the subleading terms. In particular, we focus on the contribution of the two-gluon bound state in the dual flux tube picture, proving its general form at any order in the coupling, and providing explicit expressions up to six loops. These are included in the ancillary file accompanying the version of this paper on the arXiv.

scholarly journals Two-Loop Five-Point Amplitude in N=4 Super-Yang-Mills Theory

2019 ◽  
Vol 122 (12) ◽  
Author(s):  
Samuel Abreu ◽  
Lance J. Dixon ◽  
Enrico Herrmann ◽  
Ben Page ◽  
Mao Zeng
Keyword(s):  
Yang Mills ◽  
Point Amplitude ◽  
Super Yang Mills Theory

COMMENTS ON GLUON SCATTERING AMPLITUDES IN $\mathcal{N} = 4$ SUPER YANG-MILLS THEORY AT STRONG COUPLING

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2135-2142 ◽  
Author(s):  
KATSUSHI ITO
Keyword(s):  
Scattering Amplitudes ◽  
Strong Coupling ◽  
Yang Mills ◽  
Recent Developments ◽  
Point Amplitude ◽  
Super Yang Mills Theory

We review recent developments in calculation of the gluon scattering amplitudes in [Formula: see text] super Yang-Mills theory at strong coupling via AdS/CFT correspondence. We discuss certain class of 6 and 8 point amplitudes at strong coupling, which can be obtained by cutting and gluing the 4-point amplitude.

scholarly journals The two-loop remainder function for eight and nine particles

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
John Golden ◽  
Andrew J. McLeod
Keyword(s):  
Algebraic Structure ◽  
Analytic Functions ◽  
Additive Constant ◽  
Multiplicity Results ◽  
Yang Mills ◽  
Remainder Function ◽  
Unique Decomposition ◽  
Multiple Polylogarithms ◽  
Functional Forms ◽  
Collinear Limit

Abstract Two-loop MHV amplitudes in planar $$ \mathcal{N} $$ N = 4 supersymmetric Yang Mills theory are known to exhibit many intriguing forms of cluster-algebraic structure. We leverage this structure to upgrade the symbols of the eight- and nine-particle amplitudes to complete analytic functions. This is done by systematically projecting onto the components of these amplitudes that take different functional forms, and matching each component to an ansatz of multiple polylogarithms with negative cluster-coordinate arguments. The remaining additive constant can be determined analytically by comparing the collinear limit of each amplitude to known lower-multiplicity results. We also observe that the nonclassical part of each of these amplitudes admits a unique decomposition in terms of a specific A3 cluster polylogarithm, and explore the numerical behavior of the remainder function along lines in the positive region.

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