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arXiv · 2602.11254

Quantum Gravity on AdS$_3\times$S$^3$ from CFT: Bootstrapping $n=21$

Francesco Aprile·Hynek Paul·Michele Santagata
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Abstract

We consider the simplest four-point scattering amplitude of $SO(n)$ tensor multiplets in six-dimensional (2,0) supergravity on AdS$_3\times$S$^3$. Using crossing symmetry and the consistency of the operator product expansion in the dual CFT, we explicitly construct the one-loop contribution to the correlator at order $1/c^2$, both in position space and in Mellin space. We show that a strong form of the bootstrap equations imposes constraints on the value of $n$. Remarkably, we find that our bootstrap approach uniquely determines $n=21$, which corresponds to the spectrum of IIB string theory compactified on K3. This stands in sharp contrast to the tree-level correlator for which $n$ is unconstrained. We also analyse the spectrum of unprotected double-trace operators and solve the mixing problem in the first case that involves both tensor and graviton correlators. When $n=21$, the anomalous dimensions rationalise and one of them vanishes. Lastly, we study the flat-space limit of the correlator and find perfect agreement with the one-loop amplitude recently obtained in [arXiv:2510.24558].

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Francesco Aprile, Hynek Paul, Michele Santagata. 2026-02-11. Quantum Gravity on AdS$_3\times$S$^3$ from CFT: Bootstrapping $n=21$. https://doi.org/10.1007/jhep08(2026)003

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