On the Shape of Things: From holography to elastica
arXiv:1611.03462 · doi:10.1016/j.aop.2017.08.011
Abstract
We explore the question of which shape a manifold is compelled to take when immersed in another one, provided it must be the extremum of some functional. We consider a family of functionals which depend quadratically on the extrinsic curvatures and on projections of the ambient curvatures. These functionals capture a number of physical setups ranging from holography to the study of membranes and elastica. We present a detailed derivation of the equations of motion, known as the shape equations, placing particular emphasis on the issue of gauge freedom in the choice of normal frame. We apply these equations to the particular case of holographic entanglement entropy for higher curvature three dimensional gravity and find new classes of entangling curves. In particular, we discuss the case of New Massive Gravity where we show that non-geodesic entangling curves have always a smaller on-shell value of the entropy functional. Then we apply this formalism to the computation of the entanglement entropy for dual logarithmic CFTs. Nevertheless, the correct value for the entanglement entropy is provided by geodesics. Then, we discuss the importance of these equations in the context of classical elastica and comment on terms that break gauge invariance.
arXiv comment54 pages, 8 figures. Significantly improved version, accepted for publication in Annals of Physics. New section on logarithmic CFTs. Detailed derivation of the shape equations added in appendix B. Typos corrected, clarifications added
References in corpus (33)
- Quantum entanglement
- Gauge Theory Correlators from Non-Critical String Theory
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- A Covariant Holographic Entanglement Entropy Proposal
- Geometric and Renormalized Entropy in Conformal Field Theory
- Generalized gravitational entropy
- Massive Gravity in Three Dimensions
- Logarithmic Operators in Conformal Field Theory
- Holographic Entanglement Entropy for General Higher Derivative Gravity
- Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole
- Generalized entropy and higher derivative Gravity
- Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT massive gravity
- Distributional Geometry of Squashed Cones
- Geometry of Deformations of Relativistic Membranes
- Statistical Entropy of BTZ Black Hole in Higher Curvature Gravity
- Holographic entanglement entropy and gravitational anomalies
- Entanglement Entropy of Non Unitary Conformal Field Theory
- AdS_3/LCFT_2 - Correlators in New Massive Gravity
- Four Dimensional Conformal Supergravity From AdS Space
- The Information Theoretic Interpretation of the Length of a Curve
- On entanglement entropy functionals in higher derivative gravity theories
- Confinement of semiflexible polymers
- How Fluids Bend: the Elastic Expansion for Higher-Dimensional Black Holes
- Covariant perturbations of domain walls in curved spacetime
- Conditions on holographic entangling surfaces in higher curvature gravity
- Frenet-Serret dynamics
- Entanglement Entropy for Logarithmic Conformal Field Theory
- Entanglement and mutual information in two-dimensional nonrelativistic field theories
- Blackfolds, Plane Waves and Minimal Surfaces
- Holographic entanglement entropy from minimal surfaces with/without extrinsic curvature
- Free-kick condition for entanglement entropy in higher curvature gravity
- Holographic Entanglement Entropy in NMG
- Yang-Mills theory a la string