scholarly journals MHV one-loop amplitudes in Yang-Mills from generalised unitarity

2008 ◽  
Vol 2008 (11) ◽  
pp. 078-078 ◽  
Author(s):  
Andreas Brandhuber ◽  
Massimiliano Vincon
Keyword(s):  
Yang Mills ◽  
Loop Amplitudes

scholarly journals One-loop string corrections to AdS amplitudes from CFT

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
J.M. Drummond ◽  
H. Paul
Keyword(s):  
Stress Tensor ◽  
Analytic Structure ◽  
Position Space ◽  
Yang Mills ◽  
String Corrections ◽  
The One ◽  
Loop Amplitudes

Abstract We consider α′ corrections to the one-loop four-point correlator of the stress- tensor multiplets in $$ \mathcal{N} $$ N = 4 super Yang-Mills at order 1/N4. Holographically, this is dual to string corrections of the one-loop supergravity amplitude on AdS5 × S5. While this correlator has been considered in Mellin space before, we derive the corresponding position space results, gaining new insights into the analytic structure of AdS loop amplitudes. Most notably, the presence of a transcendental weight three function involving new singularities is required, which has not appeared in the context of AdS amplitudes before. We thereby confirm the structure of string corrected one-loop Mellin amplitudes, and also provide new explicit results at orders in α′ not considered before.

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 Loop amplitudes in pure Yang-Mills from generalised unitarity

2005 ◽  
Vol 2005 (10) ◽  
pp. 011-011 ◽  
Author(s):  
Andreas Brandhuber ◽  
Simon McNamara ◽  
Bill Spence ◽  
Gabriele Travaglini
Keyword(s):  
Yang Mills ◽  
Loop Amplitudes

scholarly journals Two-loop amplitudes of gluons and octa-cuts in Script N = 4 super Yang-Mills

2005 ◽  
Vol 2005 (11) ◽  
pp. 036-036 ◽  
Author(s):  
Evgeny I Buchbinder ◽  
Freddy Cachazo
Keyword(s):  
Yang Mills ◽  
Loop Amplitudes

scholarly journals Tropical fans, scattering equations and amplitudes

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
James Drummond ◽  
Jack Foster ◽  
Ömer Gürdoğan ◽  
Chrysostomos Kalousios
Keyword(s):  
Cluster Algebras ◽  
Natural Class ◽  
Yang Mills ◽  
Kinematic Space ◽  
Super Yang Mills Theory ◽  
Loop Amplitudes

Abstract We describe a family of tropical fans related to Grassmannian cluster algebras. These fans are related to the kinematic space of massless scattering processes in a number of ways. For each fan associated to the Grassmannian Gr(k, n) there is a notion of a generalised ϕ3 amplitude and an associated set of scattering equations which further generalise the Gr(k, n) scattering equations that have been recently introduced. Here we focus mostly on the cases related to finite Grassmannian cluster algebras and we explain how face variables for the cluster polytopes are simply related to the scattering equations. For the Grassmannians Gr(4, n) the tropical fans we describe are related to the singularities (or symbol letters) of loop amplitudes in planar $$ \mathcal{N} $$ N = 4 super Yang-Mills theory. We show how each choice of tropical fan leads to a natural class of polylogarithms, generalising the notion of cluster adjacency and we describe how the currently known loop data fit into this classification.

scholarly journals Full colour for loop amplitudes in Yang-Mills theory

2017 ◽  
Vol 2017 (2) ◽  
Author(s):  
Alexander Ochirov ◽  
Ben Page
Keyword(s):  
Yang Mills ◽  
Loop Amplitudes

scholarly journals The dimension-shift conjecture for one-loop amplitudes

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Ruth Britto ◽  
Guy R. Jehu ◽  
Andrea Orta
Keyword(s):  
Loop Structure ◽  
Yang Mills ◽  
Helicity Amplitudes ◽  
The One ◽  
Loop Amplitudes

Abstract A conjecture made by Bern, Dixon, Dunbar, and Kosower asserts a simple dimension shifting relationship between the one-loop structure of $$ \mathcal{N} $$ N = 4 MHV amplitudes and all-plus helicity amplitudes in pure Yang-Mills theory. We prove this conjecture to all orders in dimensional regularisation using unitarity cuts, and evaluate the form of these simplest one-loop amplitudes using a generalised D-dimensional unitarity technique which captures the full amplitude to all multiplicities.

scholarly journals Generalized unitarity and one-loop amplitudes in super-Yang–Mills

2005 ◽  
Vol 725 (1-2) ◽  
pp. 275-305 ◽  
Author(s):  
Ruth Britto ◽  
Freddy Cachazo ◽  
Bo Feng
Keyword(s):  
Yang Mills ◽  
Loop Amplitudes

One-loop amplitudes in 𝒩 = 4 super Yang-Mills and anomalous dual conformal symmetry

2009 ◽  
Vol 2009 (08) ◽  
pp. 095-095 ◽  
Author(s):  
Andreas Brandhuber ◽  
Paul Heslop ◽  
Gabriele Travaglini
Keyword(s):  
Conformal Symmetry ◽  
Yang Mills ◽  
Loop Amplitudes
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