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

2025/12/20 by Davide Bason, Bason, Davide, Christian Copetti +7
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Advanced Operator Algebra Research #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.2512.18392

Abstract

We introduce a regularized free energy F_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.

Citations

• QCD in AdS
• Yang-Mills Flux Tube in AdS
• Higher loops in AdS: applications to boundary CFT
• Solving 1D crossing and QFT₂/CFT₁
• 1d Ising model with 1/r^1.99 interaction
• Bootstrapping the 3d Ising stress tensor
• Irreversibility of quantum field theory in de Sitter: the C, F and A theorems
• Exploring Confinement in Anti-de Sitter Space
• The defect b-theorem under bulk RG flows
• A bootstrap study of minimal model deformations
• Flat-space Partial Waves From Conformal OPE Densities
• Bootstrapping bulk locality. Part I: Sum rules for AdS form factors
• CFT in AdS and boundary RG flows
• Interpolating between a and F
• Boundary F-maximization
• AdS/CFT correspondence and Geometry

Related

• CFT in AdS and boundary RG flows
• Strongly Coupled Quantum Field Theory in Anti-de Sitter Spacetime
• The holographic F theorem
• QFT as a set of ODEs: higher dimensions
• Conformal QED in AdS as a BCFT