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Free field world-sheet correlators for ${\rm AdS}_3$
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abstract
We employ the free field realisation of the $\mathfrak{psu}(1,1|2)_1$ world-sheet theory to constrain the correlators of string theory on ${\rm AdS}_3\times {\rm S}^3\times \mathbb{T}^4$ with unit NS-NS flux. In particular, we directly obtain the unusual delta function localisation of these correlators onto branched covers of the boundary ${\rm S}^2$ by the (genus zero) world-sheet -- this is the key property which makes the equivalence to the dual symmetric orbifold manifest. In our approach, this feature follows from a remarkable `incidence relation' obeyed by the correlators, which is reminiscent of a twistorial string description. We also illustrate our results with explicit computations in various special cases.
Forward citations
Cited by 3 Pith papers
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Covering space maps for $n$-point functions with three long twists
Explicit covering-space maps for three long twists plus any number of twist-2 operators are constructed, yielding closed-form four- and five-point bare twist correlators in the ΔN=1,2 cases.
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The $\alpha$-states of a string worldsheet
The α-states of the Hurwitz worldsheet are symmetric-group characters weighted by the Poissonized Plancherel measure, so string amplitudes are ensemble averages whose weak-coupling limit is Kerov's central limit theorem.
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Remarks on Associated Varieties and Minimal Tension Holography
The associated variety of the psl(2|2) vertex algebra is identified with the cotangent bundle of the twistor space of the AdS3 boundary, and a new quotient-free free field realization of V1(psl(4|4)) is written down.
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