Regular Seminar Karthik Inbasekar (Tel Aviv U.)
room G O Jones 610
Chern-Simons theories coupled to fundamental matter have a wide variety of applications ranging from Quantum Hall effect to Quantum gravity via AdS/CFT. These theories enjoy a strong weak duality that has been tested to a very good accuracy via large N computations, such as thermal partition functions, and S matrices. Supersymmetric Chern-Simons theories are equally interesting since they have a self duality and relate to non-supersymmetric theories via RG flows. In the N=2,3 supersymmetric Chern-Simons matter theories, the four point amplitude computed to all orders in the 't Hooft coupling is not renormalised! It is a unique situation in a quantum field theory that the scattering amplitude doesn't receive loop corrections. This indicates the presence of powerful symmetry structures within the theory. This also suggests that higher point amplitudes may be easier to compute using four point amplitudes as building blocks. These higher point amplitudes not only serve as a testing tool for duality but also a probe into the symmetry structure of the theory. As a first step towards this goal, we begin by computing arbitrary n point tree level amplitudes in the N=2 theory via BCFW recursion relations. We then show that the four point tree level amplitude enjoys a dual superconformal symmetry. Since the all loop four point amplitude is tree level exact, it follows that the dual superconformal symmetry is exact to all loops. This is in contrast to highly supersymmetric examples such as N=4 SYM and N=6 ABJM, where the dual superconformal symmetry is in general anomalous. Furthermore, we show that the superconformal and dual superconformal symmetries generate an infinite dimensional Yangian symmetry for the four point amplitude. If these symmetries persist to higher point amplitudes, this suggests that the N=2 superconformal Chern-Simons matter theory may be integrable.