scholarly journals Heptagon functions and seven-gluon amplitudes in multi-Regge kinematics

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Lance J. Dixon ◽  
Yu-Ting Liu ◽  
Julian Miczajka
Keyword(s):  
Scattering Amplitudes ◽  
Series Expansion ◽  
Yang Mills ◽  
Multiple Polylogarithms ◽  
Bootstrap Approach ◽  
Mellin Representation ◽  
Regge Limit ◽  
Logarithmic Accuracy ◽  
Super Yang Mills Theory

Abstract We compute all 2 → 5 gluon scattering amplitudes in planar $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory in the multi-Regge limit that is sensitive to the non-trivial (“long”) Regge cut. We provide the amplitudes through four loops and to all logarithmic accuracy at leading power, in terms of single-valued multiple polylogarithms of two variables. To obtain these results, we leverage the function-level results for the amplitudes in the Steinmann cluster bootstrap. To high powers in the series expansion in the two variables, our results agree with the recently conjectured all-order central emission vertex used in the Fourier-Mellin representation of amplitudes in multi-Regge kinematics. Our results therefore provide a resummation of the Fourier-Mellin residues into single-valued polylogarithms, and constitute an important cross-check between the bootstrap approach and the all-orders multi-Regge proposal.

scholarly journals A tale of two Regge limits

2018 ◽  
Vol 192 ◽  
pp. 00009
Author(s):  
Vittorio Del Duca
Keyword(s):  
Scattering Amplitudes ◽  
Mathematical Structure ◽  
Yang Mills ◽  
Regge Limit ◽  
Super Yang Mills Theory

In light of the strong advances in understanding the mathematical structure of scattering amplitudes, we discuss the Regge limit of QCD and of the N = 4 Super Yang-Mills theory.

scholarly journals Spectral parameters for scattering amplitudes in $ \mathcal{N} $ =4 super Yang-Mills theory

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Livia Ferro ◽  
Tomasz Lukowski ◽  
Carlo Meneghelli ◽  
Jan Plefka ◽  
Matthias Staudacher
Keyword(s):  
Scattering Amplitudes ◽  
Spectral Parameters ◽  
Yang Mills ◽  
Super Yang Mills Theory

scholarly journals Multi-Regge limit of the two-loop five-point amplitudes in $$ \mathcal{N} $$ = 4 super Yang-Mills and $$ \mathcal{N} $$ = 8 supergravity

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Simon Caron-Huot ◽  
Dmitry Chicherin ◽  
Johannes Henn ◽  
Yang Zhang ◽  
Simone Zoia
Keyword(s):  
Reference Point ◽  
Functional Form ◽  
Transcendental Function ◽  
Effective Theory ◽  
Perfect Agreement ◽  
Yang Mills ◽  
Analytic Expressions ◽  
Regge Limit ◽  
Independent Calculation ◽  
Super Yang Mills Theory

Abstract In previous work, the two-loop five-point amplitudes in $$ \mathcal{N} $$ N = 4 super Yang-Mills theory and $$ \mathcal{N} $$ N = 8 supergravity were computed at symbol level. In this paper, we compute the full functional form. The amplitudes are assembled and simplified using the analytic expressions of the two-loop pentagon integrals in the physical scattering region. We provide the explicit functional expressions, and a numerical reference point in the scattering region. We then calculate the multi-Regge limit of both amplitudes. The result is written in terms of an explicit transcendental function basis. For certain non-planar colour structures of the $$ \mathcal{N} $$ N = 4 super Yang-Mills amplitude, we perform an independent calculation based on the BFKL effective theory. We find perfect agreement. We comment on the analytic properties of the amplitudes.

Dual superconformal symmetry of scattering amplitudes in super-Yang–Mills theory

2010 ◽  
Vol 828 (1-2) ◽  
pp. 317-374 ◽  
Author(s):  
J.M. Drummond ◽  
J. Henn ◽  
G.P. Korchemsky ◽  
E. Sokatchev
Keyword(s):  
Scattering Amplitudes ◽  
Superconformal Symmetry ◽  
Yang Mills ◽  
Super Yang Mills Theory

scholarly journals Gluing operation and form factors of local operators in N = 4 Super Yang-Mills theory

2018 ◽  
Vol 177 ◽  
pp. 09004
Author(s):  
A.E. Bolshov
Keyword(s):  
Scattering Amplitudes ◽  
Stress Tensor ◽  
Form Factors ◽  
Tensor Operator ◽  
Yang Mills ◽  
Local Operators ◽  
Non Local ◽  
Super Yang Mills Theory

The gluing operation is an effective way to get form factors of both local and non-local operators starting from different representations of on-shell scattering amplitudes. In this paper it is shown how it works on the example of form factors of operators from stress-tensor operator supermultiplet in Grassmannian and spinor helicity representations.

scholarly journals Yang–Baxter operators and scattering amplitudes in N=4 super-Yang–Mills theory

2014 ◽  
Vol 881 ◽  
pp. 467-501 ◽  
Author(s):  
D. Chicherin ◽  
S. Derkachov ◽  
R. Kirschner
Keyword(s):  
Scattering Amplitudes ◽  
Yang Mills ◽  
Super Yang Mills Theory

scholarly journals Gravity loop integrands from the ultraviolet

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Alex Edison ◽  
Enrico Herrmann ◽  
Julio Parra-Martinez ◽  
Jaroslav Trnka
Keyword(s):  
Scattering Amplitudes ◽  
Momentum Space ◽  
Indirect Evidence ◽  
Tree Level ◽  
Large Momentum ◽  
Recursion Relations ◽  
Yang Mills ◽  
The One ◽  
Geometric Picture ◽  
Super Yang Mills Theory

We demonstrate that loop integrands of (super-)gravity scattering amplitudes possess surprising properties in the ultraviolet (UV) region. In particular, we study the scaling of multi-particle unitarity cuts for asymptotically large momenta and expose an improved UV behavior of four-dimensional cuts through seven loops as compared to standard expectations. For N=8 supergravity, we show that the improved large momentum scaling combined with the behavior of the integrand under BCFW deformations of external kinematics uniquely fixes the loop integrands in a number of non-trivial cases. In the integrand construction, all scaling conditions are homogeneous. Therefore, the only required information about the amplitude is its vanishing at particular points in momentum space. This homogeneous construction gives indirect evidence for a new geometric picture for graviton amplitudes similar to the one found for planar N=4 super Yang-Mills theory. We also show how the behavior at infinity is related to the scaling of tree-level amplitudes under certain multi-line chiral shifts which can be used to construct new recursion relations.

scholarly journals The Grassmannian for celestial superamplitudes

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Livia Ferro ◽  
Robert Moerman
Keyword(s):  
Scattering Amplitudes ◽  
Correlation Functions ◽  
Minkowski Spacetime ◽  
Tree Level ◽  
Two Dimensional ◽  
Yang Mills ◽  
Celestial Sphere ◽  
Geometric Picture ◽  
Super Yang Mills Theory ◽  
The Way

Abstract Recently, scattering amplitudes in four-dimensional Minkowski spacetime have been interpreted as conformal correlation functions on the two-dimensional celestial sphere, the so-called celestial amplitudes. In this note we consider tree-level scattering amplitudes in $$ \mathcal{N} $$ N = 4 super Yang-Mills theory and present a Grassmannian formulation of their celestial counterparts. This result paves the way towards a geometric picture for celestial superamplitudes, in the spirit of positive geometries.

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