Integrability in AdS3/CFT2 and the Conformal Field Theory of the Higgs branch

Abstract:

In the context of the AdS3/CFT2 correspondence, we investigate the CFT2 at the
origin of the Higgs branch. 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 CFT2 spin-chain matches precisely the one that
was previously found as the weak-coupling limit of the integrable system describing
the AdS3 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 CFT2 side of the correspondence.