Spin chains in N = 2 superconformal theories from the ℤ₂ quiver to superconformal QCD

In this paper we find preliminary evidence that N = 2 superconformal QCD, the SU(N_c) SYM theory with N_f = 2N_c fundamental hypermultiplets, might be integrable in the large N Veneziano limit. We evaluate the one-loop dilation operator in the scalar sector of the N = 2 superconformal quiver with SU(N_c) ×SU(N_č) gauge group, for N_c = N_č. Both gauge couplings g and ǧ are exactly marginal. This theory interpolates between the Z ₂ orbifold of N = 4 SYM, which corresponds to ǧ = g, and N = 2 superconformal QCD, which is obtained for ǧ → 0. The planar one-loop dilation operator takes the form of a nearest-neighbor spin-chain Hamiltonian. For superconformal QCD the spin chain is of novel form: besides the color-adjoint fields phi;_b^a, which occupy individual sites of the chain, there are "dimers" Q_i ^aQ̄_bⁱ of flavor-contracted fundamental fields, which occupy two neighboring sites. We solve the two-body scattering problem of magnon excitations and study the spectrum of bound states, for general ǧ/g. The dimeric excitations of superconformal QCD are seen to arise smoothly for ǧ → 0 as the limit of bound wavefunctions of the interpolating theory. Finally we check the Yang-Baxter equation for the two-magnon S-matrix. It holds as expected at the orbifold point ǧ = g. While violated for general ǧ ≠ g, it holds again in the limit ǧ → 0, hinting at one-loop integrability of planar N = 2 superconformal QCD.