String Theory Seminar

# Non-planar Scattering Amplitude — Wilson Loop Duality

## by Dr. Alexander Tumanov (Tel Aviv University)

Tuesday, November 13, 2018 from to (Europe/Berlin)
at DESY ( SR3 )
 Description Higher order corrections in the 1/N expansion to scattering amplitudes come from the diagrams with higher genus. One way to address these non-trivial topologies is to view them as planar objects glued into non-planar configurations. They can then be "cut" across all the cycles of the corresponding Riemann surface, fixing the momentum flowing in each cycle. This procedure results in a planar object that belongs to a representation of the modular group of the Riemann surface in question. Various techniques developed for the planar amplitudes can be generalized to these cut non-planar ones. We will investigate the scattering amplitude — Wilson loop duality, specifically focusing on the case of the first non-planar correction, 1/N double trace amplitude, which has the topology of a cylinder. It’s dual space interpretation is a correlator of two infinite Wilson lines subject to a periodicity constraint. We will confirm this duality by a weak coupling perturbative calculation and a strong coupling string worldsheet one. This will allow us to construct the non-planar loop integrands and the BCFW recursion relation they satisfy, as well as to find an interpretation of the dual conformal symmetry in the non-planar sector, which was previously thought to be broken by 1/N corrections. Lastly, we will discuss this result in the framework of the Wilson Loop OPE approach, which allows one to compute expectation values of Wilson loops at any value of the coupling in the form of an expansion around the collinear limit. We claim that this approach can be directly applied to cut non-planar scattering amplitudes, as well as the N=4 SYM form factors, whose dual space interpretation is remarkably similar to the one of the 1/N amplitude correction.