Relative entropy and the RG flow

Abstract

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 $\Delta$ of the perturbation that triggers the RG flow.

27 pages, 2 figures

References in corpus (15)

• Towards a derivation of holographic entanglement entropy
• Seeing a c-theorem with holography
• Relative entropy and the Bekenstein bound
• Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
• The g-theorem and quantum information theory
• Some Calculable Contributions to Entanglement Entropy
• Relative Entropies in Conformal Field Theory
• Universality in the geometric dependence of Renyi entropy
• Relative entropy of excited states in two dimensional conformal field theories
• Entanglement Entropy for Relevant and Geometric Perturbations
• Area terms in entanglement entropy
• Universal Thermal Corrections to Entanglement Entropy for Conformal Field Theories on Spheres
• Renyi entropy, stationarity, and entanglement of the conformal scalar
• Entanglement entropy, planar surfaces, and spectral functions
• The Edge of Entanglement: Getting the Boundary Right for Non-Minimally Coupled Scalar Fields

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