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) x SU(N. c) gauge group, for N-c N-c. Both gauge couplings g and g are exactly marginal. This theory interpolates between the Z(2) orbifold of N = 4 SYM, which corresponds to g = g, and N = 2 superconformal QCD, which is obtained for g -> 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(a)(b), which occupy individual sites of the chain, there are dimers Q(b)(a)(Q) over bar (i)(b) 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 g/g. The dimeric excitations of superconformal QCD are seen to arise smoothly for g -> 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 g = g. While violated for general g not equal g, it holds again in the limit g -> 0, hinting at one-loop integrability of planar N = 2 superconformal QCD.