Unitarity, Crossing Symmetry and Duality in the scattering of ${\cal N}=1$ Susy Matter Chern-Simons theories

TL;DR

This paper computes the exact S-matrix for a class of ${ m N}=1$ supersymmetric Chern-Simons theories with matter, demonstrating unitarity, duality, and modified crossing symmetry, with implications for understanding strong-weak coupling dualities.

Contribution

It provides the first all-orders S-matrix computation for ${ m N}=1$ supersymmetric Chern-Simons matter theories, confirming duality and proposing modifications to crossing symmetry rules.

Findings

S-matrix matches strong-weak duality predictions

Unitarity requires modified crossing symmetry rules

Presence of a zero-mass pole on a duality surface

Abstract

We study the most general renormalizable ${\cal N}=1$ $U(N)$ Chern-Simons gauge theory coupled to a single (generically massive) fundamental matter multiplet. At leading order in the 't Hooft large $N$ limit we present computations and conjectures for the $2 \times 2$ $S$ matrix in these theories; our results apply at all orders in the 't Hooft coupling and the matter self interaction. Our $S$ matrices are in perfect agreement with the recently conjectured strong weak coupling self duality of this class of theories. The consistency of our results with unitarity requires a modification of the usual rules of crossing symmetry in precisely the manner anticipated in arXiv:1404.6373, lending substantial support to the conjectures of that paper. In a certain range of coupling constants our $S$ matrices have a pole whose mass vanishes on a self dual codimension one surface in the space of couplings.