Beyond the Planar Limit in ABJM
Robert de Mello Koch, Badr Awad Elseid Mohammed, Jeff Murugan and, Andrea Prinsloo
TL;DR
This paper constructs a complete basis of scalar operators in U(N)X U(N) gauge theories, enabling the analysis of non-planar anomalous dimensions and revealing integrability beyond the planar limit in ABJM theory.
Contribution
It introduces a comprehensive set of operators diagonalizing two-point functions at all orders in 1/N, facilitating non-planar integrability analysis in ABJM.
Findings
Operators diagonalize two-point functions at all orders in 1/N
Dilatatation operator reduces to decoupled harmonic oscillators
Evidence of integrability beyond the planar limit
Abstract
In this article we consider gauge theories with a U(N)X U(N) gauge group. We provide, for the first time, a complete set of operators built from scalar fields that are in the bi fundamental of the two groups. Our operators diagonalize the two point function of the free field theory at all orders in 1/N. We then use this basis to investigate non-planar anomalous dimensions in the ABJM theory. We show that the dilatation operator reduces to a set of decoupled harmonic oscillators, signaling integrability in a nonplanar large N limit.
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