A cosmic superfluid phase

The universe may have undergone a superfluid-like phase during its evolution, resulting from the injection of nontopological charge into the spontaneously broken vacuum. In the presence of vortices this charge is identified with angular momentum. This leads to turbulent domains on the scale of the correlation length. By restoring the symmetry at low temperatures, the vortices dissociate and push the charges to the boundaries of these domains. The model can be scaled (phenomenologically) to very low energies, it can be incorporated in a late time phase transition and form large scale structure in the boundary layers of the correlation volumes. The novel feature of the model lies in the fact that the dark matter is endowed with coherent motion. The possibilities of identifying this flow around superfluid vortices with the observed large scale bulk motion is discussed. If this identification is possible, then the definite prediction can be made that a more extended map of peculiar velocities would have to reveal large scale circulations in the flow pattern

On Volumes of Subregions in Holography and Complexity

The volume of the region inside the bulk Ryu-Takayanagi surface is a codimension-one object, and a natural generalization of holographic complexity to the case of subregions in the boundary QFT. We focus on time-independent geometries, and study the properties of this volume in various circumstances. We derive a formula for computing the volume for a strip entangling surface and a general asymptotically AdS bulk geometry. For an AdS black hole geometry, the volume exhibits non-monotonic behaviour as a function of the size of the entangling region (unlike the behaviour of the entanglement entropy in this setup, which is monotonic). For setups in which the holographic entanglement entropy exhibits transitions in the bulk, such as global AdS black hole, geometries dual to confining theories and disjoint entangling surfaces, the corresponding volume exhibits a discontinuous finite jump at the transition point (and so do the volumes of the corresponding entanglement wedges). We compute this volume discontinuity in several examples. Lastly, we compute the codim-zero volume and the bulk action of the entanglement wedge for the case of a sphere entangling surface and pure AdS geometry.Comment: 25 page

Japanese Monarchy: Past and Present

Shillony: Paper examines how Japan's imperial dynasty dependent on the male line of succession has lasted so long and analyses how it will overcome its present difficulties. An Advisory Panel was created to recommend future policy to the Koizumi cabinet but its report in 2005 was criticized. The impasse over the Panel's report was broken by the birth of a son in September 2006 to Princess Kiko, wife of Prince Akishino Best: Paper explains why the royal relationship with Japan became so important to Britain. During the Anglo-Japanese Alliance (1902-23), relations between the two Courts were cordial. The ending of the alliance did not lead to immediate substantial change. But as political relations deteriorated in the 'thirties, Court diplomacy did not yield important results, though officials continued experimenting.Shillony: Japanese Emperor, Japanese reigning empresses, concubines, collateral princely families, Imperial Household Laws, Koizumi, Advisory Panel on Succession, Crown Prince Akihito, Princess Masako, Prince Hisahito.Best: Anglo-Japanese Alliance, Order of the Garter, Emperor Hirohito, Prince of Wales, Prince Takamatsu, Prince Chichibu.

Renormalization group flow of entanglement entropy on spheres

We explore entanglement entropy of a cap-like region for a generic quantum field theory residing in the Bunch-Davies vacuum on de Sitter space. Entanglement entropy in our setup is identical with the thermal entropy in the static patch of de Sitter, and we derive a simple relation between the vacuum expectation value of the energy-momentum tensor trace and the RG flow of entanglement entropy. In particular, renormalization of the cosmological constant and logarithmic divergence of the entanglement entropy are interrelated in our setup. We confirm our findings by recovering known universal contributions for a free field theory deformed by a mass operator as well as obtain correct universal behaviour at the fixed points. Simple examples of entanglement entropy flows are elaborated in $d=2,3,4$. In three dimensions we find that while the renormalized entanglement entropy is stationary at the fixed points, it is not monotonic. We provide a computational evidence that the universal `area law' for a conformally coupled scalar is different from the known result in the literature, and argue that this difference survives in the limit of flat space. Finally, we carry out the spectral decomposition of entanglement entropy flow and discuss its application to the F-theorem.Comment: 38 pages, 2 figures; v2: references added, version accepted to JHE

Holographic Entanglement Entropy of Multiple Strips

We study holographic entanglement entropy (HEE) of $m$ strips in various holographic theories. We prove that for $m$ strips with equal lengths and equal separations, there are only 2 bulk minimal surfaces. For backgrounds which contain also "disconnected" surfaces, there are only 4 bulk minimal surfaces. Depending on the length of the strips and separation between them, the HEE exhibits first order "geometric" phase transitions between bulk minimal surfaces with different topologies. We study these different phases and display various phase diagrams. For confining geometries with $m$ strips, we find new classes of "disconnected" bulk minimal surfaces, and the resulting phase diagrams have a rich structure. We also study the "entanglement plateau" transition, where we consider the BTZ black hole in global coordinates with 2 strips. It is found that there are 4 bulk minimal surfaces, and the resulting phase diagram is displayed. We perform a general perturbative analysis of the $m$-strip system: including perturbing the CFT and perturbing the length or separation of the strips.Comment: 32 pages; v2: citations adde