Dual conformal symmetry and iterative integrals in six dimensions
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Springer
Received: March 31, 2020 Accepted: May 28, 2020 Published: June 30, 2020
L.V. Bork,a,b,e R.M. Iakhibbaev,a D.I. Kazakova,c and D.M. Tolkacheva,d a
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, st. Joliot-Curie 6, Dubna, Russia b Alikhanov Institute for Theoretical and Experimental Physics, st. Bol’shaya Cheremushkinskaya 25, Moscow, Russia c Moscow Institute of Physics and Technology, Institutskiy Pereulok 9, Dolgoprudny, Russia d Stepanov institute of Physics, Independence ave. 68, Minsk, Belarus e The Center for Fundamental and Applied Research, All-Russia Research Institute of Automatics, st. Sushchevskaya 22, Moscow, Russia
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: In this article, we continue the investigation of [1] regarding iterative properties of dual conformal integrals in higher dimensions. In d = 4, iterative properties of four and five point dual conformal integrals manifest themselves in the famous BDS ansatz conjecture. In [1] it was also conjectured that a similar structure of integrals may reappear in d = 6. We show that one can systematically, order by order in the number of loops, construct combinations of d = 6 integrals with 1/(p2 )2 propagators with an iterative structure similar to the d = 4 case. Such combinations as a whole also respect dual conformal invariance but individual integrals may not. Keywords: Scattering Amplitudes, Supersymmetric Gauge Theory, Field Theories in Higher Dimensions ArXiv ePrint: 2002.05479
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)186
JHEP06(2020)186
Dual conformal symmetry and iterative integrals in six dimensions
Contents 1 Introduction
1
2 Dual conformal symmetry
3
4 Iterative structure of the integrals
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5 Conclusion
15
A 1-loop box diagrams
15
B 2-loop box diagrams
17
1
Introduction
Study of the S-matrix (the scattering amplitudes) in supersymmetric gauge theories has revealed the existence of hidden symmetries and unexpected properties of this type of objects. It appears that the S-matrix often exhibits symmetries that are hidden from the point of view of the standard Lagrangian formulation of the theory. Applying modern methods for computing the on-shell scattering amplitudes, it is possible to learn more about the S-matrix of many theories even without direct reference to their Lagrangians using only symmetry considerations (see, for example, [2, 3] for review). Dual conformal invariance of N=4 SYM is a canonical example of such hidden symmetries [4]. It imposes very powerful constraints on the S-matrix of N=4 SYM in the planar limit [4, 5]. One of the manifestations of these powerful constraints is a very limited set of master integrals contributing to the n-point amplitudes at the low loop level [6, 7]. In addition, it was pointed out that such integrals have an iterative structure [6]. These observations culminated in the famous BDS conjecture [6] for the MHV planar amplitudes in N
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