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Home page > PhD fellowships > Previous Calls > Proposed PhD subjects 2013-2016 > Amplitudes and Integrability in supersymmetric gauges theories

Amplitudes and Integrability in supersymmetric gauges theories

by Yannis Karyotakis - 25 February 2013

Topics :  Amplitudes and integrability in supersymmetric gauges theories
Proponents : Emeri Sokatchev 
Address : LAPTH - 9 chemin de Bellevue - BP 110 - 74941 Annecy-le-Vieux cedex
Phone : +33 4 50 09 17 95 
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In the past few years several remarkable developments took place opening new perspectives in the study of scattering amplitudes. It is now possible to obtain higher-order results in perturbative gauge theory bypassing the inefficient Feynman diagram expansion. Most of this concerned the maximally supersymmetric N=4 Yang-Mills theory. Although the N=4 SYM Lagrangian differs from that of QCD, the two gauge theories share many common features. Understanding the properties and developing new calculation methods for N=4 SYM has direct relevance for QCD and for the Standard Model.
A surprising connection between gluon scattering amplitudes in N=4 SYM at strong coupling and string theory was discovered and then extended to weak coupling, as a duality between scattering amplitudes and light-like Wilson loops. This is very strong evidence for integrability of planar N=4 SYM. Integrable models are common in two-dimensional theories. We can now say that N=4 SYM is an excellent candidate for a completely integrable four-dimensional system. An example is the so-called cusp anomalous dimension, an observable appearing in many physical processes. An integral equation for the cusp anomalous dimension as a function of the coupling was derived. It interpolates smoothly between weak and strong coupling. If N=4 SYM is integrable, it has to do with hidden dynamical symmetries. An encouraging example is the surprising dual superconformal symmetry of the N=4 SYM planar scattering amplitudes. Another aspect of integrability is the planar spectrum of anomalous dimensions of Wilson operators. It is integrable up to 4 loops, and there are many signs that this persists to all orders. Especially interesting would be to see the origins of integrability on the gauge side and the way how countless non-trivial planar Feynman graphs could be summed in such a concise way. This could also lead to the verification of the whole hypothesis of the AdS/CFT correspondence.
Gravity scattering amplitudes can be computed as squares of Yang-Mills amplitudes, therefore the special features of the latter are bound to have interesting consequences for quantum (super)gravity. 
The proposed subject is not only on mathematical physics. In particular, the so-called BFKL limit of N=4 SYM is identical to that of QCD, suggesting an interesting perspective of application of SYM integrability to hadron physics. Some of the above results have already found applications to the practical problem of computing the Standard Model background for the CERN Large Hadron Collider. The LHC is expected to uncover the mechanism of the electroweak symmetry breaking, through the search of the Higgs boson and the discovery of new physics. However, this will only be possible if one has good predictions of the rates for the standard model processes that would often overwhelm the signatures of the new physics. The predictions require very heavy calculations at tree level and beyond. Higher-order contributions involve loop corrections and contributions with extra real emissions. Their practical calculation is a heavily time consuming task, for which an efficient automation exploiting an improved knowledge of the properties of the amplitudes is urgently needed.