Beyond the Tensionless Limit: Integrability in the Symmetric Orbifold

Abstract

The symmetric orbifold of ${\mathbb{T}}^4$ is exactly dual to string theory on ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathbb{T}}^4$ with minimal ($k=1$) NS-NS flux. In this paper we study the perturbation of the symmetric orbifold that is dual to switching on R-R flux, and hence to deforming the theory away from the tensionless point. More specifically, we determine systematically the action of a centrally extended supersymmetry algebra on the CFT states, and deduce from it the anomalous conformal dimensions. In the $w$-twisted sector with large $w$ the structure is similar to what was found for $\mathcal{N}=4$ SYM: the basic excitations are multi-magnons whose individual dispersion relation is fixed by symmetry, and the comparison with the BMN answer suggests that the result is true to all orders in perturbation theory. Finally we show that the multi-magnon states interact via an integrable $S$-matrix and possess a natural family of bound states.

36+18 pages, 2 figures; v2: modified the discussion in Section 6.2, added references; v3: added footnote 10, expanded discussion, rephrased various footnotes, fixed typos

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Cited by in corpus (4)

• Perturbed symmetric-product orbifold: first-order mixing and puzzles for integrability
• Mellin amplitudes for $Ad{S}_3\times S^3$
• Space-time symmetry from the world-sheet
• The Resolved Elliptic Genus and the D1-D5 CFT