Quantum Spectral Curve for AdS${}_3$/CFT${}_2$: a proposal

Abstract

We conjecture the Quantum Spectral Curve equations for string theory on $Ad{S}_3\times S^3\times T^4$ with RR charge and its CFT${}_2$ dual. We show that in the large-length regime, under additional mild assumptions, the QSC reproduces the Asymptotic Bethe Ansatz equations for the massive sector of the theory, including the exact dressing phases found in the literature. The structure of the QSC shares many similarities with the previously known AdS${}_5$ and AdS${}_4$ cases, but contains a critical new feature - the branch cuts are no longer quadratic. Nevertheless, we show that much of the QSC analysis can be suitably generalised producing a self-consistent system of equations. While further tests are necessary, particularly outside the massive sector, the simplicity and self-consistency of our construction suggests the completeness of the QSC.

31 pages + 3 appendices, 6 figures. v2: typos corrected and some comments added. Matches the version published in JHEP. v3: Note added at the end of the introduction on the form of the dressing phases. The rest of the article matches the published version, with minor typos corrected

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