Irreversibility, QNEC, and defects

Abstract

We first present an analysis of infinitesimal null deformations for the entanglement entropy, which leads to a major simplification of the proof of the $C$, $F$ and $A$-theorems in quantum field theory. Next, we study the quantum null energy condition (QNEC) on the light-cone for a CFT. Finally, we combine these tools in order to establish the irreversibility of renormalization group flows on planar $d$-dimensional defects, embedded in $D$-dimensional conformal field theories. This proof completes and unifies all known defect irreversibility theorems for defect dimensions $d\le 4$. The F-theorem on defects ($d=3$) is a new result using information-theoretic methods. For $d\ge 4$ we also establish the monotonicity of the relative entropy coefficient proportional to $R^{d-4}$. The geometric construction connects the proof of irreversibility with and without defects through the QNEC inequality in the bulk, and makes contact with the proof of strong subadditivity of holographic entropy taking into account quantum corrections.

arXiv comment26 pages, 1 figure

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• Temporal Entanglement Entropy as a probe of Renormalization Group Flow
• Aspects of Non-Relativistic Quantum Field Theories
• Non-invertible symmetries and boundaries in four dimensions
• Holographic Weyl Anomalies for 4d Defects in 6d SCFTs
• Duality transformations and the entanglement entropy of gauge theories
• Splitting interfaces in 4d $\mathcal{N}=4$ SYM
• Defects, Rigid Holography and $C$-theorems
• Holographic $a$-functions and Boomerang RG Flows
• Entanglement entropy of a Rarita-Schwinger field in a sphere
• A numerical analysis of Araki-Uhlmann relative entropy in Quantum Field Theory
• Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows
• Disclinations, dislocations, and emanant flux at Dirac criticality
• Entanglement C-functions of defects and interfaces in $\mathcal{N}=4$ supersymmetric Yang-Mills theory