Strong-coupling dynamics and integrability in gauge theories – StrongInt

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 lightlike 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, starting from an asymptotic Bethe ansatz. It interpolates smoothly between weak and strong coupling. If N=4 SYM is integrable, it has to do some 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. The Y-system for the exact spectrum of anomalous dimensions of planar N=4 SYM was conjectured. It is an infinite system of nonlinear integral equations which can be analyzed numerically or analytically in various strong and weak coupling limits. This is a huge advance compared to the Feynman graph functional integration techniques. Even better, one can reduce this infinite Y-system to a finite system of non-linear integral equations. Such a system would be desirable from many points of view: it would facilitate the numerical computations of the spectrum of operators in N=4 SYM, it might help to derive the Y-system of AdS/CFT, which currently has the status of a working conjecture. Especially interesting would be to see the origins of integrability on the gauge side and the way how these 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. Our project 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 our 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.