Holographic c-theorems in arbitrary dimensions

Abstract

We re-examine holographic versions of the c-theorem and entanglement entropy in the context of higher curvature gravity and the AdS/CFT correspondence. We select the gravity theories by tuning the gravitational couplings to eliminate non-unitary operators in the boundary theory and demonstrate that all of these theories obey a holographic c-theorem. In cases where the dual CFT is even-dimensional, we show that the quantity that flows is the central charge associated with the A-type trace anomaly. Here, unlike in conventional holographic constructions with Einstein gravity, we are able to distinguish this quantity from other central charges or the leading coefficient in the entropy density of a thermal bath. In general, we are also able to identify this quantity with the coefficient of a universal contribution to the entanglement entropy in a particular construction. Our results suggest that these coefficients appearing in entanglement entropy play the role of central charges in odd-dimensional CFT's. We conjecture a new c-theorem on the space of odd-dimensional field theories, which extends Cardy's proposal for even dimensions. Beyond holography, we were able to show that for any even-dimensional CFT, the universal coefficient appearing the entanglement entropy which we calculate is precisely the A-type central charge.

62 pages, 4 figures, few typo's corrected

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• Renormalized Entanglement Entropy on Cylinder
• RG Flow and Thermodynamics of Causal Horizons in AdS
• Holographic entanglement entropy inequalities beyond strong subadditivity
• Holographic RG flows on Squashed $S^3$
• Fermion Fields in BTZ Black Hole Space-Time and Entanglement Entropy
• $c$-functions in Higher-derivative Flows Across Dimensions
• Nonequilibrium thermodynamics perspectives for the monotonicity of the renormalization group flow
• Chiral Virasoro algebra from a single wavefunction
• Holographic Aspects of Quasi-topological Gravity
• Conical defects and holography in topological AdS gravity
• Higher-Curvature Gravity, Black Holes and Holography
• Domain Walls in Extended Lovelock Gravity
• Spatial Anisotropy in Nonrelativistic Holography
• Topological Entropy and Renormalization Group flow in 3-dimensional spherical spaces
• AdS${}_3$ black holes with primary Proca hair from a regularized Gauss-Bonnet coupling
• Entanglement Entropy of the N=4 SYM spin chain
• Localized thermal states and negative energy
• Interacting CFTs for all couplings: Thermal versus Entanglement Entropy at Large $N$
• On the Holographic Entanglement Entropy for Non-smooth Entangling Curves in AdS(4)
• String amplitudes and mutual information in confining backgrounds: the partonic behavior
• Quantum many-body physics from a gravitational lens
• Non-Perturbative Constraints on Light Sparticles from Properties of the RG Flow
• Relative Entropy and Torsion Coupling
• Holographic CFTs on $Ad{S}_d\times S^n$ and conformal defects
• Classical double copy in the black hole mini-superspace
• Note On The Dilaton Effective Action And Entanglement Entropy
• Stability of $SU(N_c)$ QCD3 from the $\epsilon$-Expansion
• Shape dependence of mutual information in the OPE limit: linear responses
• Topological perspective on bulk boundary thermodynamic equivalence
• Holographic renormalization group flows in two-dimensional gravity and $AdS$ black holes
• Zoology of heterotic supercurrent supermultiplets in d=2
• Entanglement Rényi entropies in celestial holography
• Evidence for C-theorems in 6D SCFTs
• Gauged $\mathcal{N}=3,D=4$ Supergravity: a new web of marginally connected vacua
• Black hole entropy and long strings
• A Holographic c-Theorem for Schrodinger Spacetimes
• Entanglement Entropy of $(2+1)$D Quantum Critical Points with Quenched Disorder: Dimensional Reduction Approach
• Notes on Entanglement Entropy in String Theory
• Universal corner contributions to entanglement negativity
• Mass and angular momentum of black holes in 3D gravity theories with first order formalism
• Holographic RG Flows from Quasi-Topological Gravity
• Thermodynamics of static solutions in (n+1)-dimensional Quintic Quasitopological gravity
• Holography and Conformal Anomaly Matching
• Correlation functions in expanding universes
• Some properties of the de Sitter black holes in three dimensional spacetime
• Monotonicity of RG flow in emergent dual holography of worldsheet nonlinear $\sigma$ model
• Explicit Entropic Proofs of Irreversibility Theorems for Holographic RG Flows
• Holographic complexity of rotating black holes
• Fermionic skyrmions and bosonization for a Gross-Neveu transition
• Topological Entanglement Entropy, Ground State Degeneracy and Holography
• Holographic JT gravity with quartic couplings
• Relevant perturbation of entanglement entropy of singular surfaces
• Curved Corner Contribution to the Entanglement Entropy in an Anisotropic Spacetime
• The Holographic Contributions to the Sphere Free Energy
• Holography, Fractals and the Weyl Anomaly
• The a-theorem for the four-dimensional gauged vector model
• Information Theoretic Inequalities as Bounds in Superconformal Field Theory
• Entanglement entropies of an interval in the free Schrödinger field theory at finite density
• Holographic QFTs on S${}^2\times$S${}^2$, spontaneous symmetry breaking and Efimov saddle points
• Entanglement C-functions of defects and interfaces in $\mathcal{N}=4$ supersymmetric Yang-Mills theory
• AdS/CFT correspondence for the $O(N)$ invariant critical ${\phi }^4$ model in 3-dimensions by the conformal smearing
• Entanglement Entropy Evolution under Double-trace Deformation
• Running of the Number of Degrees of Freedom in Quantum Conformal Gravity
• Quantum Field Theory on spherical space forms
• Holographic c-Function
• The a-theorem for the four-dimensional vector model
• Probing sine dilaton gravity with flow central charge
• Tenfold Way for Holography : AdS/CFT and Beyond
• Kinematics of Horizon and Singularity and IR/UV Mixing in AdS
• Position dependence of the holographic entanglement entropy for an accelerating quark-antiquark pair
• Aspects of three-dimensional higher-curvature gravities
• Holographic entanglement renormalisation for fermionic quantum matter
• Quantum information measures and their applications in quantum field theory
• Non-perturbative Aspects of Quantum Field Theories from Holography
• Extended First Law for Entanglement Entropy in Lovelock Gravity