Locality constraints in AdS$_2$ without parity

TL;DR

This paper investigates the constraints of bulk locality in AdS$_2$ quantum field theories, deriving new sum rules and bounds, and testing them in free scalar field models, addressing unique challenges due to the lower-dimensional setting.

Contribution

It introduces novel locality sum rules and dispersion relations specific to AdS$_2$, overcoming the limitations of higher-dimensional methods.

Findings

Established power-law bounds for correlators in AdS$_2$

Derived new symmetric and antisymmetric locality sum rules

Validated sum rules in free scalar field theory

Abstract

We study bulk locality constraints in quantum field theories in AdS$_2$. The known derivation of locality sum rules in AdS$_{d+1}$ does not apply for $d=1$ due to the different singularity structure of the conformal blocks and the inequivalence of operator orderings on the boundary. Assuming unitarity and a mild growth condition, we establish power-law bounds for correlators, derive dispersion relations and an expansion in terms of ``even'' and ``odd'' local blocks that converges in the entire AdS$_2$. These yield two novel families of symmetric and antisymmetric locality sum rules. We test these sum rules explicitly in the free scalar field theory.