Bogdan Stoica

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

A bstractTwo-dimensional conformal field theories exhibit a universal free energy in the high temperature limit T → ∞, and a universal spectrum in the Cardy regime, Δ → ∞. 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≥c6

Locality of Gravitational Systems from Entanglement of Conformal Field Theories

Delta ge frac{c}{6}

Spontaneous Generation of Angular Momentum in Holographic Theories

. 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.

Hall viscosity and angular momentum in gapless holographic models

A bstractWe 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.

Edge length dynamics on graphs with applications to p-adic AdS/CFT

Jennifer Lin, Matilde Marcolli, Hirosi Ooguri, 4 and Bogdan Stoica Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago, IL 60637 Department of Mathematics, California Institute of Technology, 253-37, Pasadena, CA 91125 Walter Burke Institute for Theoretical Physics, California Institute of Technology, 452-48, Pasadena, CA 91125 Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa 277-8583, Japan (Dated: December 8, 2014)

Angular Momentum Generation by Parity Violation

In this paper we argue that classical asymptotically anti-de Sitter spacetimes that arise as states in consistent ultraviolet completions of Einstein gravity coupled to matter must satisfy an infinite family of positive energy conditions. To each ball-shaped spatial region B of the boundary spacetime we can associate a bulk spatial region Σ_B between B and the bulk extremal surface nB nwith the same boundary as B. We show that there exists a natural notion of a gravitational energy for every such region that is non-negative, and non-increasing as one makes the region smaller. The results follow from identifying this gravitational energy with a quantum relative entropy in the associated dual conformal field theory state. The positivity and monotonicity properties of the gravitational energy are implied by the positivity and monotonicity of relative entropy, which holds universally in all quantum systems.

Tensor networks,

The Schwarzschild black two-brane in four-dimensional anti-dexa0Sitter 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-Nordström 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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We use the holographic approach to compare the Hall viscosity η_H and the angular momentum density 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 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 J receives contributions from degrees of freedom at all scales.