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In the context of the AdS$_3$/CFT$_2$ correspondence, we investigate theHiggs branch CFT$_2$. Witten showed that states localised near the smallinstanton singularity can be described in terms of vector multiplet variables.This theory has a planar, weak-coupling limit, in which anomalous dimensions ofsingle-trace composite operators can be calculated. At one loop, thecalculation reduces to finding the spectrum of a spin-chain withnearest-neighbour interactions. This CFT$_2$ spin-chain matches precisely theone that was previously found as the weak-coupling limit of the integrablesystem describing the AdS$_3$ side of the duality. We compute the one-loopdilatation operator in a non-trivial compact subsector and show that itcorresponds to an integrable spin-chain Hamiltonian. This provides the firstdirect evidence of integrability on the CFT$_2$ side of the correspondence.

Integrability and the Conformal Field Theory of the Higgs branch