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

TL;DR

This paper derives an exact four-point scattering amplitude for a non-relativistic superconformal Chern-Simons theory, demonstrating trivial scattering at specific levels and confirming quantum conformal invariance through explicit calculations.

Contribution

It provides the first exact all-order four-point scattering amplitude for this superconformal theory and verifies its properties through one-loop computations.

Findings

Scattering amplitude becomes trivial at levels k=1 and 2.

Beta function for contact interaction vanishes at one-loop.

Amplitude matches explicit field theory calculations.

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.