Poles in the S-matrix of relativistic Chern-Simons matter theories from quantum mechanics

An all orders formula for the S-matrix for 2 → 2 scattering in large N Chern- Simons theory coupled to a fundamental scalar has recently been conjectured. We find a scaling limit of the theory in which the pole in this S-matrix is near threshold. We argue that the theory must be well described by non-relativistic quantum mechanics in this limit, and determine the relevant Schroedinger equation. We demonstrate that the S-matrix obtained from this Schroedinger equation agrees perfectly with this scaling limit of the relativistic S-matrix; in particular the pole structures match exactly. We view this matching as a nontrivial consistency check of the conjectured field theory S-matrix.