Poles in the $S$-Matrix of Relativistic Chern-Simons Matter theories from Quantum Mechanics

Understand

An all orders formula for the $S$-matrix for 2 $\rightarrow$ 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.