Dispersive Sum Rules in AdS$_2$

TL;DR

This paper develops dispersive sum rules for 1D CFTs in AdS$_2$, deriving bounds on higher-derivative couplings in weakly-coupled EFTs, and explores the effects of finite AdS radius on these bounds.

Contribution

It introduces dispersive sum rules for 1D CFTs in AdS$_2$ and derives bounds on higher-derivative couplings, including finite AdS radius effects.

Findings

Bounds on higher-derivative couplings in AdS$_2$ EFTs match flat-space results at leading order.

Explicit formula for anomalous dimensions in AdS$_2$ Witten diagrams.

Finite AdS radius modifies the bounds on couplings.

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$_2$.