Scattering Amplitude and Bosonization Duality in General Chern-Simons Vector Models

TL;DR

This paper computes exact four-point functions and scattering amplitudes in large N Chern-Simons vector models, revealing dualities, unusual crossing, and non-relativistic limits, with implications for unitarity and phase structure.

Contribution

It provides the first exact large N calculation of four-point functions and S-matrices in general Chern-Simons bosonic and fermionic vector models, demonstrating dualities and novel scattering features.

Findings

S-matrix exhibits bosonization duality and unusual crossing relations.

Identifies a pole in the S-matrix related to coupling constants.

Shows non-relativistic limit reduces to Aharonov-Bohm scattering.

Abstract

We present exact large N calculus of four point function in general Chern-Simons bosonic and fermionic vector models. Applying the LSZ formula to the four point function we determine two body scattering amplitudes in these theories taking a special care for a non-analytic term to achieve unitarity in the singlet channel. We show that the S-matrix enjoys the bosonization duality, unusual crossing relation and non-relativistic reduction to Aharonov-Bohm scattering. We also argue that the S-matrix develops a pole in a certain range of coupling constants, which disappears in the range where the theory reduces to Chern-Simons theory interacting with free fermions.