Exact 4-point Scattering Amplitude of the Superconformal Schrodinger Chern-Simons Theory

Abstract

We consider the non-relativistic superconformal U(N) X U(N) Chern-Simons theory with level (k,-k) possessing fourteen supersymmetries. We obtain an exact four-point scattering amplitude of the theory to all orders in 1/N and 1/k and prove that the scattering amplitude becomes trivial when k=1 and 2. We confirm this amplitude to one-loop order by using an explicit field theoretic computation and show that the beta function for the contact interaction vanishes to the one-loop order, which is consistent with the quantum conformal invariance of the underlying theory.