Einstein–Gauss–Bonnet black holes in de Sitter spacetime and the quasilocal formalism

We propose to compute the action and global charges of the asymptotically de Sitter solutions in Einstein–Gauss–Bonnet theory by using the counterterm method in conjunction with the quasilocal formalism. The general expression of the counterterms and the boundary stress tensor is presented for spacetimes of dimension d?7$d?7$. We apply this technique for several different solutions in Einstein–Gauss–Bonnet theory with a positive cosmological constant. Apart from known solutions, we consider also d=5$d=5$ vacuum rotating black holes with equal magnitude angular momenta. These solutions are constructed numerically within a nonperturbative approach, by directly solving the Einstein–Gauss–Bonnet equations with suitable boundary conditions.     

Higher-order singletons,partially massless fields,and their boundary values in the ambient approach

Using ambient space we develop a fully gauge and o(d,2)$\mathfrak{o}(d,2)$-covariant approach to boundary values of _AdSd+1${\mathit{AdS}}_{d+1}$ gauge fields. It is applied to the study of (partially) massless fields in the bulk and (higher-order) conformal scalars, i.e. singletons, as well as (higher-depth) conformal gauge fields on the boundary. In particular, we identify the corresponding generalized Fradkin–Tseytlin equations as obstructions to the extension of the off-shell boundary value to the bulk, generalizing the usual considerations for the holographic anomalies to the partially massless fields. We also relate the background fields for the higher-order singleton to the boundary values of partially massless fields and prove the appropriate generalization of the Flato–Fronsdal theorem, which is in agreement with the known structure of symmetries for the higher-order wave operator. All these facts support the following generalization of the higher-spin holographic duality: the O(N)$O(N)$ model at a multicritical isotropic Lifshitz point should be dual to the theory of partially massless symmetric tensor fields described by the Vasiliev equations based on the higher-order singleton symmetry algebra.     

Various types of phase transitions in the AdS soliton background

We study the basic holographic insulator and superconductor phase transition in the AdS soliton background by generalizing the spontaneous breaking of a global U(1)$\mathrm{U}(1)$ symmetry to occur via Stückelberg mechanism. We construct the soliton solutions with backreaction and examine the effects of the backreaction on the condensation of the scalar hair in the generalized Stückelberg Lagrangian. We disclose rich physics in various phase transitions. In addition to the AdS soliton configuration, we also examine the property of the phase transition in the AdS black hole background.     

Superconformal invariants or how to relate four-point AdS amplitudes

Using the form of N=2$N=2$ superconformal invariants we derive the explicit relation between the bottom and top components of the correlator of four stress-tensor multiplets in N=4$N=4$ super-Yang–Mills. The result is given in terms of an eighth order differential operator acting on the function of two variables which characterises these correlators. It allows us to show a non-trivial consistency relation between the known results for the corresponding supergravity amplitudes on AdS₅${\mathit{AdS}}_5$.     

Weyl anomaly of conformal higher spins on six-sphere

This paper is a sequel to arXiv:1309.0785 were we computed the Weyl anomaly a   (Euler density or logarithmic divergence on S^d$S^d$) coefficient for higher-derivative conformal higher spin field in d=4$d=4$ and shown that it matches the expression found in arXiv:1306.5242 by a “holographic” method from a ratio of massless higher spin determinants in AdS₅. Here we repeat the same computation in on 6-sphere and demonstrate that the result matches again the one following from AdS₇. We also discuss explicitly similar matching in the d=2$d=2$ case.     

Ricci dark energy in braneworld models with a Gauss–Bonnet term in the bulk

We investigate the Ricci Dark Energy (RDE) in the braneworld models with a Gauss–Bonnet term in the Bulk. We analytically solve the generalized Friedmann equation on the brane and find that the universe will finally enter into a pure de Sitter spacetime in stead of the big rip that appears in the usual 4D Ricci dark energy model with parameter α<1/2$\alpha <1/2$. We also consider the Hubble horizon as the IR cutoff in holographic dark energy model and find it cannot accelerate the universe as in the usual case without interacting.     

Entanglement entropy of round spheres

We propose that the logarithmic term in the entanglement entropy computed in a conformal field theory for a (d−2)$(d-2)$-dimensional round sphere in Minkowski spacetime is identical to the logarithmic term in the entanglement entropy of extreme black hole. The near horizon geometry of the latter is H₂×S_d−2$H_2\times S_{d-2}$. For a scalar field this proposal is checked by direct calculation. We comment on relation of this and earlier calculations to the “brick wall” model of 't Hooft. The case of generic 4d conformal field theory is discussed.     

A study on the relations between the topological parameter and entanglement

In this Letter, some relations between the topological parameter d   and concurrences of the projective entangled states have been presented. It is shown that for the case with d=n$d=n$, all the projective entangled states of two n  -dimensional quantum systems are the maximally entangled states (i.e. C=1$C=1$). And for another case with d≠n$d\ne n$, C   both approach 0 when d→+∞$d\to +\infty$ for n=2$n=2$ and 3. Then we study the thermal entanglement and the entanglement sudden death (ESD) for a kind of Yang–Baxter Hamiltonian. It is found that the parameter d   influences not only the critical temperature _Tc$T_c$ but also the maximum entanglement value that the system can arrive at. And we also find that the parameter d has a great influence on the ESD.     

General holographic superconductor models with Gauss–Bonnet corrections

We study general models for holographic superconductors in Einstein–Gauss–Bonnet gravity. We find that different values of Gauss–Bonnet correction term and model parameters can determine the order of phase transitions and critical exponents of second-order phase transitions. Moreover we find that the size and strength of the conductivity coherence peak can be controlled. The ratios ωg/Tc${\omega }_g/Tc$ for various model parameters have also been examined.     

Spinning black strings in five-dimensional Einstein–Gauss–Bonnet gravity

We construct generalizations of the D=5$D=5$ Kerr black string by including higher curvature corrections to the gravity action in the form of the Gauss–Bonnet density. These uniform black strings satisfy a generalized Smarr relation and share the basic properties of the Einstein gravity solutions. However, they exist only up to a maximal value of the Gauss–Bonnet coupling constant, which depends on the solutions? mass and angular momentum.     

Entanglement entropy and variational methods: Interacting scalar fields

We develop a variational approximation to the entanglement entropy for scalar ?⁴${?}^4$ theory in 1+1$1+1$, 2+1$2+1$, and 3+1$3+1$ dimensions, and then examine the entanglement entropy as a function of the coupling. We find that in 1+1$1+1$ and 2+1$2+1$ dimensions, the entanglement entropy of ?⁴${?}^4$ theory as a function of coupling is monotonically decreasing and convex. While ?⁴${?}^4$ theory with positive bare coupling in 3+1$3+1$ dimensions is thought to lead to a trivial free theory, we analyze a version of ?⁴${?}^4$ with infinitesimal negative bare coupling, an asymptotically free theory known as precarious  ?⁴${?}^4$ theory, and explore the monotonicity and convexity of its entanglement entropy as a function of coupling. Within the variational approximation, the stability of precarious ?⁴${?}^4$ theory is related to the sign of the first and second derivatives of the entanglement entropy with respect to the coupling.     

Quantum corrections to Bekenstein–Hawking black hole entropy and gravity partition functions

Algebraic aspects of the computation of partition functions for quantum gravity and black holes in _AdS3${\mathit{AdS}}_3$ are discussed. We compute the sub-leading quantum corrections to the Bekenstein–Hawking entropy. It is shown that the quantum corrections to the classical result can be included systematically by making use of the comparison with conformal field theory partition functions, via the _AdS3/_CFT2${\mathit{AdS}}_3/{\mathit{CFT}}_2$ correspondence. This leads to a better understanding of the role of modular and spectral functions, from the point of view of the representation theory of infinite-dimensional Lie algebras. Besides, the sum of known quantum contributions to the partition function can be presented in a closed form, involving the Patterson–Selberg spectral function. These contributions can be reproduced in a holomorphically factorized theory whose partition functions are associated with the formal characters of the Virasoro modules. We propose a spectral function formulation for quantum corrections to the elliptic genus from supergravity states.     

Non-extensive statistical entropy,quantum groups and quantum entanglement

In this work, we explore a new connection between quantum groups and Tsallis entropy through the energy spectrum of a Hamiltonian with S_Uq(2)$S{U}_q\left(2\right)$ symmetry. Identifying the deformation parameter of the entropy with the parameter of deformation of the associated quantum group, we deduce Tsallis entropy for states related to such a system with S_Uq(2)$S{U}_q\left(2\right)$ symmetry and conducted an investigation of quantum entanglement.     

Higher dimensional Yang–Mills black holes in third order Lovelock gravity

By employing the higher (N>5$N>5$)-dimensional version of the Wu–Yang ansatz we obtain magnetically charged new black hole solutions in the Einstein–Yang–Mills–Lovelock (EYML) theory with second (α₂${\alpha }_2$) and third (α₃${\alpha }_3$) order parameters. These parameters, where α₂${\alpha }_2$ is also known as the Gauss–Bonnet parameter, modify the horizons (and the resulting thermodynamical properties) of the black holes. It is shown also that asymptotically (r→∞$r\to \infty$), these parameters contribute to an effective cosmological constant—without cosmological constant—so that the solution behaves de-Sitter (anti de-Sitter) like.     

Quantum spherical model with competing interactions

We analyse the phase diagram of a quantum mean spherical model in terms of the temperature T$T$, a quantum parameter g$g$, and the ratio p=−_J2/_J1$p=-J_2/J_1$, where _J1>0$J_1>0$ refers to ferromagnetic interactions between first-neighbour sites along the d$d$ directions of a hypercubic lattice, and _J2<0$J_2<0$ is associated with competing antiferromagnetic interactions between second neighbours along m≤d$m\le d$ directions. We regain a number of known results for the classical version of this model, including the topology of the critical line in the g=0$g=0$ space, with a Lifshitz point at p=1/4$p=1/4$, for d>2$d>2$, and closed-form expressions for the decay of the pair correlations in one dimension. In the T=0$T=0$ phase diagram, there is a critical border, _gc=_gc(p)$g_c=g_c\left(p\right)$ for d≥2$d\ge 2$, with a singularity at the Lifshitz point if d<(m+4)/2$d<(m+4)/2$. We also establish upper and lower critical dimensions, and analyse the quantum critical behavior in the neighborhood of p=1/4$p=1/4$.