Integrability and the conformal field theory of the Higgs branch

Abstract

Abstract: In the context of the AdS 3 /CFT 2 correspondence, we investigate the Higgs branch CFT 2. Witten showed that states localised near the small instanton singularity can be described in terms of vector multiplet variables. This theory has a planar, weak-coupling limit, in which anomalous dimensions of single-trace composite operators can be calculated. At one loop, the calculation reduces to finding the spectrum of a spin-chain with nearest-neighbour interactions. This CFT 2 spin-chain matches precisely the one that was previously found as the weak-coupling limit of the integrable system describing the AdS 3 side of the duality. We compute the one-loop dilatation operator in a non-trivial compact subsector and show that it corresponds to an integrable spin-chain Hamiltonian. This provides the first direct evidence of integrability on the CFT 2 side of the correspondence.