Locality constraints in AdS${}_2$ without parity

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.

25 pages + appendix, 5 figures; published version (added and updated discussions, reference added)