scholarly journals N=4 supersymmetric Yang–Mills scattering amplitudes at high energies: the Regge cut contribution

2009 ◽  
Vol 65 (3-4) ◽  
pp. 587-605 ◽  
Author(s):  
J. Bartels ◽  
L. N. Lipatov ◽  
A. Sabio Vera
Keyword(s):  
Scattering Amplitudes ◽  
Yang Mills ◽  
High Energies

scholarly journals Algebraic singularities of scattering amplitudes from tropical geometry

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
James Drummond ◽  
Jack Foster ◽  
Ömer Gürdoğan ◽  
Chrysostomos Kalousios
Keyword(s):  
Scattering Amplitudes ◽  
Natural Language ◽  
Tropical Geometry ◽  
Cluster Algebras ◽  
Finite Alphabet ◽  
Square Root ◽  
Finite Sets ◽  
Yang Mills ◽  
Square Roots ◽  
Algebraic Singularities

Abstract We address the appearance of algebraic singularities in the symbol alphabet of scattering amplitudes in the context of planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory. We argue that connections between cluster algebras and tropical geometry provide a natural language for postulating a finite alphabet for scattering amplitudes beyond six and seven points where the corresponding Grassmannian cluster algebras are finite. As well as generating natural finite sets of letters, the tropical fans we discuss provide letters containing square roots. Remarkably, the minimal fan we consider provides all the square root letters recently discovered in an explicit two-loop eight-point NMHV calculation.

scholarly journals Two-loop rational terms in Yang-Mills theories

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Jean-Nicolas Lang ◽  
Stefano Pozzorini ◽  
Hantian Zhang ◽  
Max F. Zoller
Keyword(s):  
Scattering Amplitudes ◽  
Gauge Theories ◽  
A Posteriori ◽  
Four Dimensions ◽  
Yang Mills ◽  
General Properties ◽  
Finite Set ◽  
Numerical Tools ◽  
Loop Amplitudes

Abstract Scattering amplitudes in D dimensions involve particular terms that originate from the interplay of UV poles with the (D − 4)-dimensional parts of loop numerators. Such contributions can be controlled through a finite set of process-independent rational counterterms, which make it possible to compute loop amplitudes with numerical tools that construct the loop numerators in four dimensions. Building on a recent study [1] of the general properties of two-loop rational counterterms, in this paper we investigate their dependence on the choice of renormalisation scheme. We identify a nontrivial form of scheme dependence, which originates from the interplay of mass and field renormalisation with the (D−4)-dimensional parts of loop numerators, and we show that it can be controlled through a new kind of one-loop counterterms. This guarantees that the two-loop rational counterterms for a given renormalisable theory can be derived once and for all in terms of generic renormalisation constants, which can be adapted a posteriori to any scheme. Using this approach, we present the first calculation of the full set of two-loop rational counterterms in Yang-Mills theories. The results are applicable to SU(N) and U(1) gauge theories coupled to nf fermions with arbitrary masses.

scholarly journals Celestial superamplitude in $$ \mathcal{N} $$ = 4 SYM theory

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Hongliang Jiang
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Scattering Amplitudes ◽  
Momentum Space ◽  
Ward Identity ◽  
Yang Mills ◽  
Conformal Field ◽  
New Perspective ◽  
Celestial Sphere

Abstract Celestial amplitude is a new reformulation of momentum space scattering amplitudes and offers a promising way for flat holography. In this paper, we study the celestial amplitudes in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills (SYM) theory aiming at understanding the role of superconformal symmetry in celestial holography. We first construct the superconformal generators acting on the celestial superfield which assembles all the on-shell fields in the multiplet together in terms of celestial variables and Grassmann parameters. These generators satisfy the superconformal algebra of $$ \mathcal{N} $$ N = 4 SYM theory. We also compute the three-point and four-point celestial super-amplitudes explicitly. They can be identified as the conformal correlation functions of the celestial superfields living at the celestial sphere. We further study the soft and collinear limits which give rise to the super-Ward identity and super-OPE on the celestial sphere, respectively. Our results initiate a new perspective of understanding the well-studied $$ \mathcal{N} $$ N = 4 SYM amplitudes via 2D celestial conformal field 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 Asymptotic dynamics on the worldline for spinning particles

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Domenico Bonocore
Keyword(s):  
Scattering Amplitudes ◽  
Gauge Boson ◽  
Classical Limit ◽  
Wilson Line ◽  
Background Field ◽  
Spinning Particle ◽  
Spinning Particles ◽  
Yang Mills ◽  
Asymptotic Dynamics ◽  
Gravity Theories

Abstract There has been a renewed interest in the description of dressed asymptotic states à la Faddeev-Kulish. In this regard, a worldline representation for asymptotic states dressed by radiation at subleading power in the soft expansion, known as the Generalized Wilson Line (GWL) in the literature, has been available for some time, and it recently found applications in the derivation of factorization theorems for scattering processes of phenomenological relevance. In this paper we revisit the derivation of the GWL in the light of the well-known supersymmetric wordline formalism for the relativistic spinning particle. In particular, we discuss the importance of wordline supersymmetry to understand the contribution of the soft background field to the asymptotic dynamics. We also provide a derivation of the GWL for the gluon case, which was not previously available in the literature, thus extending the exponentiation of next-to-soft gauge boson corrections to Yang-Mills theory. Finally, we comment about possible applications in the current research about asymptotic states in scattering amplitudes for gauge and gravity theories and their classical limit.

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