Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows

Abstract

We revisit the existence of monotonic quantities along renormalization group flows using only the Null Energy Condition and the Ryu-Takayanagi formula for the entanglement entropy of field theories with anti-de Sitter gravity duals. In particular, we consider flows within the same dimension and holographically reprove the $c$-, $F$-, and $a$-theorems in dimensions two, three, and four. We focus on the family of maximally spherical entangling surfaces, define a quasi-constant of motion corresponding to the breaking of conformal invariance, and use a properly defined distance between minimal surfaces to construct a holographic $c$-function that is monotonic along the flow. We then apply our method to the case of flows across dimensions: There, we reprove the monotonicity of flows from ${\mathrm{AdS}}_{D+1}$ to ${\mathrm{AdS}}_3$ and prove the novel case of flows from ${\mathrm{AdS}}_5$ to ${\mathrm{AdS}}_4$.

arXiv comment28 pages, 3 figures; references added

References in corpus (69)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Aspects of Holographic Entanglement Entropy
• Towards a derivation of holographic entanglement entropy
• Supergravity description of field theories on curved manifolds and a no go theorem
• On Renormalization Group Flows in Four Dimensions
• Conformal collider physics: Energy and charge correlations
• Holographic c-theorems in arbitrary dimensions
• Notes on Some Entanglement Properties of Quantum Field Theory
• Novel Local CFT and Exact Results on Perturbations of N=4 Super Yang Mills from AdS Dynamics
• Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy
• A finite entanglement entropy and the c-theorem
• On the RG running of the entanglement entropy of a circle
• Seeing a c-theorem with holography
• A Quantum Focussing Conjecture
• Black Holes in Quasi-topological Gravity
• A refinement of entanglement entropy and the number of degrees of freedom
• Light-ray operators in conformal field theory
• Higher Derivative Gravity, Causality and Positivity of Energy in a UV complete QFT
• A new cubic theory of gravity in five dimensions: Black hole, Birkhoff's theorem and C-function
• Averaged Null Energy Condition from Causality
• Two-dimensional SCFTs from wrapped branes and c-extremization
• Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
• Proof of the Quantum Null Energy Condition
• Energy conditions in general relativity and quantum field theory
• Comments on Holographic Entanglement Entropy and RG Flows
• M-Fivebranes Wrapped on Supersymmetric Cycles
• On the new massive gravity and AdS/CFT
• Markov property of the CFT vacuum and the a-theorem
• A c-theorem for the entanglement entropy
• On renormalization group flows and the a-theorem in 6d
• Anomalies, Renormalization Group Flows, and the a-Theorem in Six-Dimensional (1,0) Theories
• Type IIB Supergravity Solutions with AdS${}_5$ From Abelian and Non-Abelian T Dualities
• Born-Infeld extension of new massive gravity
• A General Proof of the Quantum Null Energy Condition
• Fivebranes Wrapped On Associative Three-Cycles
• Holographic Proof of the Quantum Null Energy Condition
• Membranes Wrapped on Holomorphic Curves
• Probing renormalization group flows using entanglement entropy
• Two-dimensional SCFTs from D3-branes
• Classification of Six Derivative Lagrangians of Gravity and Static Spherically Symmetric Solutions
• Compactifications of the Klebanov-Witten CFT and new $Ad{S}_3$ backgrounds
• Universal RG Flows Across Dimensions and Holography
• M-Fivebranes Wrapped on Supersymmetric Cycles II
• Relative entropy and the RG flow
• Spheres, Charges, Instantons, and Bootstrap: A Five-Dimensional Odyssey
• A holographic proof of the averaged null energy condition
• c-functions in the Born-Infeld extended New Massive Gravity
• AdS${}_7$/CFT${}_6$ with orientifolds
• T-branes, Anomalies and Moduli Spaces in 6D SCFTs
• Energy is Entanglement
• Holographic Entanglement Entropy and Renormalization Group Flow
• c-theorem of the entanglement entropy
• Irreversibility, QNEC, and defects
• On higher derivative gravity, c-theorems and cosmology
• Holographic c-theorems and higher derivative gravity
• Surface Theory: the Classical, the Quantum, and the Holographic
• Proof of the quantum null energy condition for free fermionic field theories
• Evidence for a 5d F-theorem
• Holographic c-theorem and Born-Infeld Gravity Theories
• Renormalized holographic entanglement entropy in Lovelock gravity
• C-Functions in Lovelock Gravity
• Holographic RG flows, entanglement entropy and the sum rule
• QNEC2 in deformed holographic CFTs
• 3D Lovelock Gravity and the Holographic c-Theorem
• A Holographic Study of the $a$-theorem and RG Flow in General Quadratic Curvature Gravity
• Entanglement and Topology in RG Flows Across Dimensions: Caps, Bridges and Corners
• $c$-functions in Higher-derivative Flows Across Dimensions
• Holographic entanglement entropy inequalities beyond strong subadditivity
• Higher order curvature corrections and holographic renormalization group flow