Scattering in Mass-Deformed N>=4 Chern-Simons Models

TL;DR

This paper explores the scattering matrix in mass-deformed N>=4 Chern-Simons theories, revealing its equivalence to integrability structures in AdS/CFT and the Hubbard model, supported by one-loop amplitude calculations.

Contribution

It uncovers the algebraic structure linking Chern-Simons models to integrability and Hubbard model R-matrices, providing new insights into their scattering properties.

Findings

Scattering matrix matches AdS/CFT worldsheet matrix

Scattering matrix aligns with Hubbard model R-matrix

One-loop amplitudes agree with unitarity constraints

Abstract

We investigate the scattering matrix in mass-deformed N>=4 Chern-Simons models including as special cases the BLG and ABJM theories of multiple M2 branes. Curiously the structure of this scattering matrix in three spacetime dimensions is equivalent to (a) the two-dimensional worldsheet matrix found in the context of AdS/CFT integrability and (b) the R-matrix of the one-dimensional Hubbard model. The underlying reason is that all three models are based on an extension of the psu(2|2) superalgebra which constrains the matrix completely. We also compute scattering amplitudes in one-loop field theory and find perfect agreement with scattering unitarity.