Unitarity, Crossing Symmetry and Duality of the S-matrix in large N Chern-Simons theories with fundamental matter

TL;DR

This paper computes and conjectures the structure of 2-to-2 scattering matrices in large N Chern-Simons theories with matter, revealing dualities, unusual features, and potential universal properties of these S-matrices.

Contribution

It provides explicit all-order computations of S-matrices, uncovers their duality relations, and introduces modified crossing symmetry in Chern-Simons matter theories.

Findings

S-matrices map under Bose-Fermi duality with level-rank transposition

Presence of non-analytic forward scattering terms

Modified crossing symmetry rules for these theories

Abstract

We present explicit computations and conjectures for $2 \to 2$ scattering matrices in large $N$ {\it $U(N)$} Chern-Simons theories coupled to fundamental bosonic or fermionic matter to all orders in the 't Hooft coupling expansion. The bosonic and fermionic S-matrices map to each other under the recently conjectured Bose-Fermi duality after a level-rank transposition. The S-matrices presented in this paper may be regarded as relativistic generalization of Aharonov-Bohm scattering. They have unusual structural features: they include a non analytic piece localized on forward scattering, and obey modified crossing symmetry rules. We conjecture that these unusual features are properties of S-matrices in all Chern-Simons matter theories. The S-matrix in one of the exchange channels in our paper has an anyonic character; the parameter map of the conjectured Bose-Fermi duality may be derived by equating the anyonic phase in the bosonic and fermionic theories.