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

Abstract

We study the most general renormalizable $\mathcal{N}=1$ $U(N)$ 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.

63 pages + 26 pages appendices, 6 figures, V2: Corrected typos, added references, V3: Corrected typos, added clarifications

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