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TH String Theory Seminar
A toy model for light-by-light scattering
4-3-006 - TH Conference Room (CERN)
4-3-006 - TH Conference Room
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It is well-known that the classical Kepler problem possesses a non-obvious symmetry, related to the so-called Runge-Lenz vector and responsible for the periodicity of planetary orbits. I will review the role of this symmetry in the quantum formulation of the problem, revealing its most recent incarnation within a fully consistent relativistic quantum field theory, as a nontrivial generator of the dual conformal symmetry of (planar) N=4 super Yang-Mills. This connection is made visible by considering a natural analog of light-by-light scattering in this theory, with massive particles introduced through the Higgs mechanism. I will discuss recent progress in computing massive multi-loop integrals, where we succeeded in computing analytically this analog of light-by-light scattering to three-loop order by exploiting the Runge-Lenz symmetry. I will also present a novel way to calculate the spectrum of corresponding Hydrogen-like bound states, at all values of the coupling, exploiting old ideas from Regge theory.