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Deriving the long-string CFT in AdS$_3$
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abstract
We revisit the path integral formulation of bosonic string theory in locally-AdS$_3$ spacetimes. Through a careful analysis of the worldsheet sigma model, we write down an effective theory of long strings living near the boundary of AdS$_3$. By directly computing the partition function of the long-string sector, we find that the worldsheet path integral naturally organizes itself into the Coulomb-gas expansion of a 2D conformal field theory on the asymptotic boundary, with the number of coulomb integrals being dual to the dimension of the moduli space of worldsheet instantons in the bulk. As such, we provide a derivation of the CFT dual of long strings in AdS$_3$ for completely generic spacetime and worldsheet topologies.
Forward citations
Cited by 2 Pith papers
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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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Worldsheet CFT$_2$ and Celestial CFT$_2$ : An AdS$_3$-CFT$_2$ perspective
A near-boundary scaling limit of AdS/CFT is proposed to produce celestial CFTs, and the long-string sector of string theory on AdS3 is identified as a Lorentz-only celestial CFT2.
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