Aspects of Holographic Entanglement at Finite Temperature and Chemical Potential

We investigate the behavior of entanglement entropy at finite temperature and chemical potential for strongly coupled large-N gauge theories in $d$-dimensions ($d\ge 3$) that are dual to Anti-de Sitter-Reissner-Nordstrom geometries in $(d+1)-$dimensions, in the context of gauge-gravity duality. We develop systematic expansions based on the Ryu-Takayanagi prescription that enable us to derive analytic expressions for entanglement entropy and mutual information in different regimes of interest. Consequently, we identify the specific regions of the bulk geometry that contribute most significantly to the entanglement entropy of the boundary theory at different limits. We define a scale, dubbed as the effective temperature, which determines the behavior of entanglement in different regimes. At high effective temperature, entanglement entropy is dominated by the thermodynamic entropy, however, mutual information subtracts out this contribution and measures the actual quantum entanglement. Finally, we study the entanglement/disentanglement transition of mutual information in the presence of chemical potential which shows that the quantum entanglement between two sub-regions decreases with the increase of chemical potential.Comment: 38 pages, multiple figure

Strongly-coupled anisotropic gauge theories and holography

We initiate a non-perturbative study of anisotropic, non-conformal and confining gauge theories that are holographically realized in gravity by generic Einstein-Axion-Dilaton systems. In the vacuum our solutions describe RG flows from a conformal field theory in the UV to generic scaling solutions in the IR with generic hyperscaling violation and dynamical exponents $\theta$ and $z$. We formulate a generalization of the holographic c-theorem to the anisotropic case. At finite temperature, we discover that the anisotropic deformation reduces the confinement-deconfinement phase transition temperature suggesting a possible alternative explanation of inverse magnetic catalysis solely based on anisotropy. We also study transport and diffusion properties in anisotropic theories and observe in particular that the butterfly velocity that characterizes both diffusion and growth of chaos transverse to the anisotropic direction, saturates a constant value in the IR which can exceed the bound given by the conformal value.Comment: 6 pages, 4 figures; v2: minor improvements, references added, version accepted for publication in PR

Entanglement and out-of-equilibrium dynamics in holographic models of de Sitter QFTs

In this paper we study various aspects of entanglement entropy in strongly-coupled de Sitter quantum field theories in various dimensions. We find gravity solutions that are dual to field theories in a fixed de Sitter background, both in equilibrium and out-of-equilibrium configurations. The latter corresponds to the Vaidya generalization of the AdS black hole solutions with hyperbolic topology. We compute analytically the entanglement entropy of spherical regions and show that there is a transition when the sphere is as big as the horizon. We also explore thermalization in time-dependent situations in which the system evolves from a non-equilibrium state to the Bunch-Davies state. We find that the saturation time is equal to the light-crossing time of the sphere. This behavior is faster than random walk and suggests the existence of free light-like degrees of freedom.Comment: 39 pages, 11 figures; minor changes, conclusions unchange

Branes from Light: Embeddings and Energetics for Symmetric kk-Quarks in N=4\mathcal{N}=4 SYM

We construct the D3-brane dual to a $k$-quark of $\mathcal{N}=4$ super-Yang-Mills theory in the totally symmetric representation of $SU(N)$, undergoing arbitrary motion. Our method of construction generalizes previous work by Mikhailov, and proceeds by shooting light rays inward from the anti-de Sitter boundary, to trace out the brane embedding. We expect this method to have wider relevance, and provide evidence for this by showing that it correctly reproduces the known D5-brane embeddings dual to totally antisymmetric $k$-quarks. As an application of our solutions, we compute the energy of the D3-brane and extract from it the $k$-quark's intrinsic energy and rate of radiation. The result matches expectations based on previous calculations, and makes contact with the exact Bremsstrahlung function for the fundamental representation.Comment: 1+28 pages, 3 figures. v2: references adde

Fast and Slow Coherent Cascades in Anti-de Sitter Spacetime

We study the phase and amplitude dynamics of small perturbations in 3+1 dimensional Anti-de Sitter spacetime using the truncated resonant approximation, also known as the Two Time Framework (TTF). We analyse the phase spectrum for different classes of initial data and find that higher frequency modes turn on with coherently aligned phases. Combining numerical and analytical results, we conjecture that there is a class of initial conditions that collapse in infinite slow time and to which the well-studied case of the two-mode, equal energy initial data belongs. We additionally study perturbations that collapse in finite time, and find that the energy spectrum approaches a power law, with the energy per mode scaling approximately as the inverse first power of the frequency.Comment: 19 pages, multiple figures. v2: version published in CQ