Integrability and the Conformal Field Theory of the Higgs branch

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.

29 pages; v2: improved presentation and discussion, computations and results unchanged

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• The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4 with mixed three-form flux
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Cited by in corpus (2)

• The ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$ worldsheet S matrix
• Stringy Symmetries and the Higher Spin Square