On the Integrability of Planar N=2 Superconformal Gauge Theories

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.

20 pages, 1 figure. v2: minor changes, JHEP version

References in corpus (4)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• From Scattering Amplitudes to the Dilatation Generator in N=4 SYM
• From N=4 gauge theory to N=2 conformal QCD: three-loop mixing of scalar composite operators
• The Complete One-loop Spin Chain of N =1 SQCD

Cited by in corpus (14)

• Exact Bremsstrahlung and Effective Couplings
• Integrability and non-Integrability in N=2 SCFTs and their Holographic Backgrounds
• The Exact Effective Couplings of 4D N=2 gauge theories
• Integrability in N=2 superconformal gauge theories
• Large $N$ correlation functions in $\mathcal{N}=2$ superconformal quivers
• The Bremsstrahlung function of $\mathcal{N}=2$ SCQCD
• Four-point amplitudes in $\mathcal{N}=2$ SCQCD
• Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs
• Wilson loop correlators in $\mathcal{N}=2$ superconformal quivers
• Supermembrane actions for Gaiotto-Maldacena backgrounds
• Chiral correlators in $\mathcal{N}=2$ superconformal quivers
• Strong-coupling results for $\mathcal{N}=2$ superconformal quivers and holography
• On the Amplitude/Wilson Loop duality in $\mathcal{N}=2$ SCQCD
• A study on free roots of Borcherds-Kac-Moody Lie Superalgebras