Swampland Conditions for Higher Derivative Couplings from CFT

TL;DR

This paper derives bounds on higher derivative scalar couplings in AdS from conformal bootstrap principles, revealing positivity and convexity constraints that distinguish consistent effective theories from those incompatible with a UV completion.

Contribution

It provides the first analytical bounds on higher derivative couplings in AdS EFTs derived solely from CFT bootstrap axioms, including gravity effects.

Findings

Couplings with even k≥2 must satisfy positivity, monotonicity, and log-convexity.

Gravity inclusion allows negative coupling for the  interaction.

Constraints are derived from Lorentzian four-point correlators in the Regge limit.

Abstract

There are effective field theories that cannot be embedded in any UV complete theory. We consider scalar effective field theories, with and without dynamical gravity, in $D$-dimensional anti-de Sitter (AdS) spacetime with large radius and derive precise bounds (analytically) on the coupling constants of higher derivative interactions $\phi^2\Box^k\phi^2$ by only requiring that the dual CFT obeys the standard conformal bootstrap axioms. In particular, we show that all such coupling constants, for even $k\ge 2$, must satisfy positivity, monotonicity, and log-convexity conditions in the absence of dynamical gravity. Inclusion of gravity only affects constraints involving the $\phi^2\Box^2\phi^2$ interaction which now can have a negative coupling constant. Our CFT setup is a Lorentzian four-point correlator in the Regge limit. We also utilize this setup to derive constraints on effective field theories of multiple scalars. We argue that similar analysis should impose nontrivial constraints on the graviton four-point scattering amplitude in AdS.