Dispersive Sum Rules in AdS${}_2$

Abstract

Dispersion relations for S-matrices and CFT correlators translate UV consistency into bounds on IR observables. In this note, we construct dispersive sum rules for 1D CFTs. We use them to prove bounds on higher-derivative couplings in weakly-coupled non-gravitational EFTs in AdS${}_2$. At the leading order in the bulk-point limit, the bounds agree with the flat-space result. We compute the leading universal effect of finite AdS radius on the bounds. Along the way, we give an explicit formula for anomalous dimensions in general higher-derivative contact Witten diagrams in AdS${}_2$.

v2: minor changes to introduction, figures updated, references added

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Cited by in corpus (7)

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• Polyakov blocks for the 1D CFT mixed correlator bootstrap
• Large $N$ analytical functional bootstrap I: 1D CFTs and total positivity
• 1d Conformal Field Theory and Dispersion Relations
• Moments and saddles of heavy CFT correlators