arXiv subjects

Bogdan Stoica

Publications and source records attributed to Bogdan Stoica.

24 records · Page 2Linked to original sources

arXiv2015

The Holographic Entropy Cone

We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.

hep-th↗

arXiv2014

Tomography from Entanglement

The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of a minimal surface in its holographic dual. We show that this relation can be inverted for any state in the conformal field theory to compute the bulk stress-energy tensor near the boundary of the bulk spacetime, reconstructing the local data in the bulk from the entanglement on the boundary. We also show that positivity, monotonicity, and convexity of the relative entropy for small spherical domains between the reduced density matrices of any state and of the ground state of the conformal field theory, follow from positivity conditions on the bulk matter energy density. We discuss an information theoretical interpretation of the convexity in terms of the Fisher metric.

hep-th↗

arXiv2014

Universal Spectrum of 2d Conformal Field Theory in the Large c Limit

Two-dimensional conformal field theories exhibit a universal free energy in the high temperature limit $T \to \infty$, and a universal spectrum in the Cardy regime, $Δ\to \infty$. We show that a much stronger form of universality holds in theories with a large central charge $c$ and a sparse light spectrum. In these theories, the free energy is universal at all values of the temperature, and the microscopic spectrum matches the Cardy entropy for all $Δ\geq c/6$. The same is true of three-dimensional quantum gravity; therefore our results provide simple necessary and sufficient criteria for 2d CFTs to behave holographically in terms of the leading spectrum and thermodynamics. We also discuss several applications to CFT and gravity, including operator dimension bounds derived from the modular bootstrap, universality in symmetric orbifolds, and the role of non-universal `enigma' saddlepoints in the thermodynamics of 3d gravity.

hep-th↗

arXiv2014

Angular Momentum Generation by Parity Violation

We generalize our holographic derivation of spontaneous angular momentum generation in 2 + 1 dimensions in several directions. We consider cases when a parity violating perturbation responsible for the angular momentum generation can be non-marginal (while in our previous paper we restricted to a marginal perturbation), including all possible two-derivative interactions, with parity violations triggered both by gauge and gravitational Chern-Simons terms in the bulk. We make only a minimal assumption about the bulk geometry that it is asymptotically AdS, respects the Poincaré symmetry in 2 + 1 dimensions, and has a horizon. In this generic setup, we find a remarkably concise and universal formula for the expectation value of the angular momentum density, to all orders in the parity violating perturbation.

hep-th↗

arXiv2014

Hall Viscosity and Angular Momentum in Gapless Holographic Models

We use the holographic approach to compare the Hall viscosity $η_H$ and the angular momentum density ${\cal J}$ in gapless systems in $2+1$ dimensions at finite temperature. We start with a conformal fixed point and turn on a perturbation which breaks the parity and time reversal symmetries via gauge and gravitational Chern-Simons couplings in the bulk. While the ratio of $η_H$ and ${\cal J}$ shows some universal properties when the perturbation is slightly relevant, we find that the two quantities behave differently in general. In particular, $η_H$ depends only on infrared physics, while ${\cal J}$ receives contributions from degrees of freedom at all scales.

hep-th↗

arXiv2013

Spontaneous Generation of Angular Momentum in Holographic Theories

The Schwarzschild black two-brane in four-dimensional anti-de Sitter space is dual to a finite temperature state in three-dimensional conformal field theory. We show that the solution acquires a nonzero angular momentum density when a gravitational Chern-Simons coupling is turned on in the bulk, even though the solution is not modified. A similar phenomenon is found for the Reissner-Nordstrom black two-brane with axionic coupling to the gauge field. We discuss interpretation of this phenomenon from the point of view of the boundary three-dimensional conformal field theory.

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