On the Integrability of Planar N=2 Superconformal Gauge Theories

TL;DR

This paper investigates the integrability of planar N=2 superconformal gauge theories, finding that certain sectors are not integrable at two loops, but some sectors may be integrable to all loops.

Contribution

It demonstrates the non-integrability of the SU(2|1) sector at two loops and proposes potential all-loop integrability of the SU(2,1|2) sector in N=2 superconformal theories.

Findings

SU(2|1) sector fails integrability at two loops

Yang-Baxter equation not satisfied in SU(2|1) sector

SU(2,1|2) sector may be integrable to all loops

Abstract

We study the integrability properties of planar N=2 superconformal field theories in four dimensions. We show that the spin chain associated to the planar dilation operator of N=2 superconformal QCD fails to be integrable at two loops. In our analysis we focus on a closed SU(2|1) sector, whose two-loop spin chain we fix by symmetry arguments (up to a few undetermined coefficients). It turns out that the Yang-Baxter equation for magnon scattering is not satisfied in this sector. On the other hand, we suggest that the closed SU(2,1|2) sector, which exists in any N=2 superconformal gauge theory, may be integrable to all loops.