Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2212.10575 · Physical Review Letters

Entropic g Theorem in General Spacetime Dimensions

Horacio Casini, Ignacio Salazar Landea, Gonzalo Torroba

Published Mar 17, 2023• 35 citations
arXivHTMLPDF

Abstract

We establish the irreversibility of renormalization group flows on a pointlike defect inserted in a d-dimensional Lorentzian conformal field theory. We identify the impurity entropy g with the quantum relative entropy in two equivalent ways. One involves a null deformation of the Cauchy surface, and the other is given in terms of a local quench protocol. Positivity and monotonicity of the relative entropy imply that g decreases monotonically along renormalization group flows, and provides a clear information-theoretic meaning for this irreversibility.

DOI
10.1103/physrevlett.130.111603

Related papers

Irreversibility in quantum field theories with boundaries

Horacio Casini, Ignacio Salazar Landea, Gonzalo Torroba

Abstract We study conformal field theories with boundaries, and their boundary renormalization group (RG) flows, using methods from quantum information theory. Positivity of the relative entropy, together with unitarity and Lorentz invariance, give rise to bounds that characterize the irreversibility of such flows. This generalizes the recently proved entropic g-theorem to higher dimensions. In 2 + 1 dimensions with a boundary, we prove the entropic b-theorem — the decrease of the two-dimensional Weyl anomaly under boundary RG flows. In higher dimensions, the bound implies that the leading area coefficient of the entanglement entropy induced by the defect decreases along the flow. Our proof unifies these properties, and provides an information-theoretic interpretation in terms of the distinguishability between the short distance and long distance states. Finally, we establish a sum rule for the change in the area term in theories with boundaries, which could have implications for models with localized gravity.

arXiv:1812.08183•Journal of High Energy Physics•Apr 1, 2019•54 citations

Relative entropy and the RG flow

Horacio Casini, Eduardo Testé, Gonzalo Torroba

We consider the relative entropy between vacuum states of two different theories: a conformal field theory (CFT), and the CFT perturbed by a relevant operator. By restricting both states to the null Cauchy surface in the causal domain of a sphere, we make the relative entropy equal to the difference of entanglement entropies. As a result, this difference has the positivity and monotonicity properties of relative entropy. From this it follows a simple alternative proof of the c-theorem in d = 2 space-time dimensions and, for d > 2, the proof that the coefficient of the area term in the entanglement entropy decreases along the renormalization group (RG) flow between fixed points. We comment on the regimes of convergence of relative entropy, depending on the space-time dimensions and the conformal dimension Δ of the perturbation that triggers the RG flow.

arXiv:1611.00016•Journal of High Energy Physics•Mar 1, 2017•67 citations

The g-theorem and quantum information theory

Horacio Casini, Ignacio Salazar Landea, Gonzalo Torroba

We study boundary renormalization group flows between boundary conformal field theories in 1 + 1 dimensions using methods of quantum information theory. We define an entropic g-function for theories with impurities in terms of the relative entanglement entropy, and we prove that this g-function decreases along boundary renormalization group flows. This entropic g-theorem is valid at zero temperature, and is independent from the g-theorem based on the thermal partition function. We also discuss the mutual information in boundary RG flows, and how it encodes the correlations between the impurity and bulk degrees of freedom. Our results provide a quantum-information understanding of (boundary) RG flow as increase of distinguishability between the UV fixed point and the theory along the RG flow.

arXiv:1607.00390•Journal of High Energy Physics•Oct 1, 2016•137 citations

Irreversibility, QNEC, and defects

Horacio Casini, Ignacio Salazar Landea, Gonzalo Torroba

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 ≤ 4. The F-theorem on defects (d = 3) is a new result using information-theoretic methods. For d ≥ 4 we also establish the monotonicity of the relative entropy coefficient proportional to Rd−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:2303.16935•Journal of High Energy Physics•Jul 3, 2023•35 citations

Renormalization Group Flows on Line Defects

Gabriel Cuomo, Zohar Komargodski, Avia Raviv-Moshe

We consider line defects in d-dimensional conformal field theories (CFTs). The ambient CFT places nontrivial constraints on renormalization group (RG) flows on such line defects. We show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions. We demonstrate our results in a flow between Wilson loops in four dimensions.

arXiv:2108.01117•Physical Review Letters•Jan 11, 2022•104 citations

Defect localized entropy: Renormalization group and holography

Ma-Ke Yuan, Yang Zhou

We consider p-dimensional defects in D-dimensional conformal field theories (CFTs) and construct defect localized entropy by performing Casini-Huerta-Myers transformation for the system with defect. The defect localized entropy is a measure of entanglement between the degrees of freedom localized on the defect. We show that at the fixed point of defect renormalization group (RG) flow, defect localized entropy is equal to minus defect free energy for universal part. We construct defect C-functions from the defect localized entropy for surface defects and volume defects, and show that they monotonically decrease in both cases following the entropic method by Casini and Huerta. We also study the holographic dual of defect localized entropy and find that it is given by the minimal surface located at string or brane worldvolume embedded in the holographic bulk.

arXiv:2209.08835•Nuclear Physics B•Jul 18, 2023•6 citations
We establish the irreversibility of renormalization group flows on a pointlike defect inserted in a d-dimensional Lorentzian conformal field theory. We identify the impurity entropy g with the quantum relative entropy in two equivalent ways. One involves a null deformation of the Cauchy surface, and the other is given in terms of a local quench protocol. Positivity and monotonicity of the relative entropy imply that g decreases monotonically along renormalization group flows, and provides a clear information-theoretic meaning for this irreversibility.
Abstract We study conformal field theories with boundaries, and their boundary renormalization group (RG) flows, using methods from quantum information theory. Positivity of the relative entropy, together with unitarity and Lorentz invariance, give rise to bounds that characterize the irreversibility of such flows. This generalizes the recently proved entropic g-theorem to higher dimensions. In 2 + 1 dimensions with a boundary, we prove the entropic b-theorem — the decrease of the two-dimensional Weyl anomaly under boundary RG flows. In higher dimensions, the bound implies that the leading area coefficient of the entanglement entropy induced by the defect decreases along the flow. Our proof unifies these properties, and provides an information-theoretic interpretation in terms of the distinguishability between the short distance and long distance states. Finally, we establish a sum rule for the change in the area term in theories with boundaries, which could have implications for models with localized gravity.
We consider the relative entropy between vacuum states of two different theories: a conformal field theory (CFT), and the CFT perturbed by a relevant operator. By restricting both states to the null Cauchy surface in the causal domain of a sphere, we make the relative entropy equal to the difference of entanglement entropies. As a result, this difference has the positivity and monotonicity properties of relative entropy. From this it follows a simple alternative proof of the c-theorem in d = 2 space-time dimensions and, for d > 2, the proof that the coefficient of the area term in the entanglement entropy decreases along the renormalization group (RG) flow between fixed points. We comment on the regimes of convergence of relative entropy, depending on the space-time dimensions and the conformal dimension Δ of the perturbation that triggers the RG flow.
We study boundary renormalization group flows between boundary conformal field theories in 1 + 1 dimensions using methods of quantum information theory. We define an entropic g-function for theories with impurities in terms of the relative entanglement entropy, and we prove that this g-function decreases along boundary renormalization group flows. This entropic g-theorem is valid at zero temperature, and is independent from the g-theorem based on the thermal partition function. We also discuss the mutual information in boundary RG flows, and how it encodes the correlations between the impurity and bulk degrees of freedom. Our results provide a quantum-information understanding of (boundary) RG flow as increase of distinguishability between the UV fixed point and the theory along the RG flow.
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 ≤ 4. The F-theorem on defects (d = 3) is a new result using information-theoretic methods. For d ≥ 4 we also establish the monotonicity of the relative entropy coefficient proportional to Rd−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.
We consider p-dimensional defects in D-dimensional conformal field theories (CFTs) and construct defect localized entropy by performing Casini-Huerta-Myers transformation for the system with defect. The defect localized entropy is a measure of entanglement between the degrees of freedom localized on the defect. We show that at the fixed point of defect renormalization group (RG) flow, defect localized entropy is equal to minus defect free energy for universal part. We construct defect C-functions from the defect localized entropy for surface defects and volume defects, and show that they monotonically decrease in both cases following the entropic method by Casini and Huerta. We also study the holographic dual of defect localized entropy and find that it is given by the minimal surface located at string or brane worldvolume embedded in the holographic bulk.