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arXiv · 1411.3676

Integrability and the Conformal Field Theory of the Higgs branch

Olof Ohlsson Sax·Alessandro Sfondrini·Bogdan Stefanski Jr
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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.

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Olof Ohlsson Sax, Alessandro Sfondrini, Bogdan Stefanski Jr. 2014-11-13. Integrability and the Conformal Field Theory of the Higgs branch. https://arxiv.org/abs/1411.3676

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