F-theorem for Quantum Field Theories in Anti-de Sitter Space

TL;DR

This paper proposes a new regularized free energy for QFTs in AdS space, conjectures its monotonicity under RG flow, and supports this with examples, proofs, and applications to critical phenomena.

Contribution

It introduces a regularized free energy in AdS, conjectures its RG monotonicity, and extends the boundary F-theorem to non-conformal theories with proofs and applications.

Findings

Conjecture of monotonic free energy under RG flow in AdS.

Proof of the conjecture in two dimensions.

Bounds on sphere free energy for Ising models.

Abstract

We introduce a regularized free energy $\mathcal{F}_{\text{AdS}}$ for massive quantum field theories (QFTs) on Anti-de Sitter space (AdS). We conjecture this quantity to be monotonic under the renormalization group (RG) flow induced by boundary perturbations, generalizing the known boundary $F$-theorem to non-conformal setups. We test this conjecture in several examples and provide a proof in two dimensions. We also discuss applications to long-range critical points, obtaining bounds on the sphere free energy of long- and short-range Ising models in three dimensions.