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<p>We consider the simplest four-point scattering amplitude of SO(<i>n</i>) tensor multiplets in six-dimensional (2,0) supergravity on AdS<sub>3</sub>×S<sup>3</sup>. 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/<i>c</i><sup>2</sup>, both in position space and in Mellin space. We show that a strong form of the bootstrap equations imposes constraints on the value of <i>n</i>. Remarkably, we find that our bootstrap approach uniquely determines <i>n</i> = 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 <i>n</i> 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 <i>n</i> = 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 [1].</p>

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Quantum gravity on AdS3×S3 from CFT: bootstrapping n = 21

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  • 出版模式：

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  • 发表日期：

    2026年8月3日

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  • Francesco Aprile,
  • Hynek Paul,
  • Michele Santagata

摘要

We consider the simplest four-point scattering amplitude of SO(n) tensor multiplets in six-dimensional (2,0) supergravity on AdS3×S3. 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/c2, 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 [1].