Proves integer Rényi QNEC by establishing log-convexity of Kosaki L^n norms under null-translation semigroups for σ-finite von Neumann algebras with half-sided modular inclusions, assuming only finite sandwiched Rényi divergence to the vacuum.
Irreversibility, QNEC, and defects
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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.
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hep-th 3representative citing papers
Relative entropy of vacuum vs coherent state for λφ⁴ in the Rindler wedge equals the classical interacting boost charge to O(λ) and obeys the Bekenstein bound.
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A general proof of integer R\'enyi QNEC
Proves integer Rényi QNEC by establishing log-convexity of Kosaki L^n norms under null-translation semigroups for σ-finite von Neumann algebras with half-sided modular inclusions, assuming only finite sandwiched Rényi divergence to the vacuum.
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Relative entropy for $\lambda \phi^4$ in the Rindler wedge
Relative entropy of vacuum vs coherent state for λφ⁴ in the Rindler wedge equals the classical interacting boost charge to O(λ) and obeys the Bekenstein bound.
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