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arXiv · 2512.18392

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

Davide Bason·Christian Copetti·Lorenzo Di Pietro·Ziming Ji·Shota Komatsu
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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.

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Davide Bason, Christian Copetti, Lorenzo Di Pietro, Ziming Ji, Shota Komatsu. 2025-12-20. F-theorem for Quantum Field Theories in Anti-de Sitter Space. https://arxiv.org/abs/2512.18392

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