O-BTZ: Orientifolded BTZ black hole

Banados–Teitelboim–Zanelli (BTZ) black holes are constructed by orbifolding AdS₃ geometry by boost transformations of its O(2,2)$O(2,2)$ isometry group. Here we construct a new class of solutions to AdS₃ Einstein gravity, orientifolded BTZ or O-BTZ   for short, which in general, besides the usual BTZ orbifolding, involve orbifolding (orientifolding) by a Z₂${\mathbb{Z}}_2$ part of O(2,2)$O(2,2)$ isometry group. This Z₂${\mathbb{Z}}_2$ is chosen such that it changes the orientation on AdS₃ while keeping the orientation on its 2D conformal boundary. O-BTZ solutions exhaust all un-oriented AdS₃ black hole solutions, as BTZ black holes constitute all oriented AdS₃ black holes. O-BTZ, similarly to BTZ black holes, are stationary, axisymmetric asymptotically AdS₃ geometries with two asymptotic charges, mass and angular momentum.     

Refined holographic entanglement entropy for the AdS solitons and AdS black holes

We consider the refinement of the holographic entanglement entropy for the holographic dual theories to the AdS solitons and AdS black holes, including the corrected ones by the Gauss–Bonnet term. The refinement is obtained by extracting the UV-independent piece of the holographic entanglement entropy, the so-called renormalized entanglement entropy which is independent of the choices of UV cutoff. Our main results are: (i) the renormalized entanglement entropies of the _AdSd+1${\mathrm{AdS}}_{d+1}$ soliton for d=4,5$d=4,5$ are neither monotonically decreasing along the RG flow nor positive-definite, especially around the deconfinement/confinement phase transition; (ii) there is no topological entanglement entropy for AdS₅ soliton even with Gauss–Bonnet correction; (iii) for the AdS black holes, the renormalized entanglement entropy obeys an expected volume law at IR regime, and the transition between UV and IR regimes is a smooth crossover even with Gauss–Bonnet correction; (iv) based on AdS/MERA conjecture, we postulate that the IR fixed-point state for the non-extremal AdS soliton is a trivial product state.     

Properties of CFTs dual to charged BTZ black hole

We study properties of strongly coupled CFT's with non-zero background electric charge in 1+1$1+1$ dimensions by studying the dual gravity theory—which is a charged BTZ black hole. Correlators of operators dual to scalars, gauge fields and fermions are studied at both T=0$T=0$ and T≠0$T\ne 0$. In the T=0$T=0$ case we are also able to compare with analytical results based on AdS₂${\mathit{AdS}}_2$ and find reasonable agreement. In particular the correlation between log periodicity and the presence of finite spectral density of gapless modes is seen. The real part of the conductivity (given by the current–current correlator) also vanishes as ω→0$\omega \to 0$ as expected. The fermion Green's function shows quasiparticle peaks with approximately linear dispersion but the detailed structure is neither Fermi liquid nor Luttinger liquid and bears some similarity to a “Fermi–Luttinger” liquid. This is expected since there is a background charge and the theory is not Lorentz or scale invariant. A boundary action that produces the observed non-Luttinger liquid like behavior (k  -independent non-analyticity at ω=0$\omega =0$) in the Green's function is discussed.     

On the anatomy of multi-spin magnon and single spike string solutions

We study rigid string solutions rotating in AdS₅×S⁵${\mathit{AdS}}_5\times S^5$ background. For particular values of the parameters of the solutions we find multispin solutions corresponding to giant magnons and single spike strings. We present an analysis of the dispersion relations in the case of three spin solutions distributed only in S⁵$S^5$ and the case of one spin in AdS₅${\mathit{AdS}}_5$ and two spins in S⁵$S^5$. The possible relation of these string solutions to gauge theory operators and spin chains are briefly discussed.     

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${\mathit{AdS}}_5$.     

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.     

Ultraviolet behaviour of higher spin gauge field propagators and one loop mass renormalization

The ultraviolet singular structure of the bulk-to-bulk propagators for higher spin gauge fields in AdS₄${\mathit{AdS}}_4$ space is analyzed in details. Possible interactions with the Higgs scalar and the corresponding one loop mass renormalization are studied. This mass renormalization is finite and connected with the anomalous dimensions of those currents in the corresponding boundary CFT₃${\mathit{CFT}}_3$ that cease to be conserved when the interaction is switched on. In particular it is proportional to ?−2$?-2$.     

Some properties of the Alday–Maldacena minimum

The Alday–Maldacena solution, relevant to the n=4$n=4$ gluon amplitude in N=4$N=4$ SYM at strong coupling, was recently identified as a minimum of the regularized action in the moduli space of solutions of the AdS₅${\mathit{AdS}}_5$σ  -model equations of motion. Analogous solutions of the Nambu–Goto equations for the n=4$n=4$ case are presented and shown to form (modulo the reparametrization group) an equally large but different moduli space, with the Alday–Maldacena solution at the intersection of the σ  -model and Nambu–Goto moduli spaces. We comment upon the possible form of the regularized action for n=5$n=5$. A function of moduli parameters za$z_a$ is written, whose minimum reproduces the BDDK one-loop five-gluon amplitude. This function may thus be considered as some kind of Legendre transform of the BDDK formula and has its own value independently of the Alday–Maldacena approach.     

Exact expressions for quantum corrections to spinning strings

The one-loop worldsheet quantum corrections to the energy of spinning strings on R×S³$\mathbb{R}\times S^3$ within AdS₅×S⁵${\mathit{AdS}}_5\times S^5$ are reexamined. The explicit expansion in the effective 't Hooft coupling λ^′=λ/J²${\lambda }^{\prime }=\lambda /J^2$ is rigorously derived. The expansion contains both analytic and non-analytic terms in λ^′${\lambda }^{\prime }$, as well as exponential corrections. Furthermore, we pin down the origin of the terms that are not captured by the quantum string Bethe ansatz, which only produces analytic terms in λ^′${\lambda }^{\prime }$. It is shown that the analytic terms arise from string fluctuations within the S³$S^3$, whereas the non-analytic and exponential terms, which are not captured by the Bethe ansatz, originate from the fluctuations in all directions within the supersymmetric sigma model on AdS₅×S⁵${\mathit{AdS}}_5\times S^5$. We also comment on the case of spinning string in AdS₃×S¹${\mathit{AdS}}_3\times S^1$.     

Regular black hole remnants in de Sitter space

We address the question of thermodynamical evolution of regular spherically symmetric cosmological black holes with de Sitter center. Space–time is asymptotically de Sitter as r→0$r\to 0$ and as r→∞$r\to \infty$. A source term in the Einstein equations connects smoothly two de Sitter vacua with different values of cosmological constant and corresponds to anisotropic vacuum dark fluid defined by symmetry of its stress–energy tensor. In the range of masses M_cr1?M?M_cr2$M_{cr1}?M?M_{cr2}$ it describes a regular cosmological black hole with three horizons, an internal horizon ra$r_a$, a black hole horizon rb>ra$r_b>r_a$, and a cosmological horizon rc>rb$r_c>r_b$. Thermodynamical preference for a final product of evaporation is a double-horizon (ra=rb$r_a=r_b$) black hole remnant with the positive specific heat.     

Central charges in 2d reduced cosmological massive gravity

In the dimensionally reduced model of the (2+1)$(2+1)$-dimensional cosmological massive gravity, we obtain the central charges of the two types of the black hole based on the entropy function method. One is for the BTZ black hole and the other one is actually for the warped AdS₃ black hole.     

Three PT-symmetric Hamiltonians with completely different spectra

We discuss three Hamiltonians, each with a central-field part H₀$H_0$ and a PT-symmetric perturbation igz$igz$. When H₀$H_0$ is the isotropic Harmonic oscillator the spectrum is real for all g$g$ because H$H$ is isospectral to H₀+g²/2$H_0+g^2/2$. When H₀$H_0$ is the Hydrogen atom then infinitely many eigenvalues are complex for all g$g$. If the potential in H₀$H_0$ is linear in the radial variable r$r$ then the spectrum of H$H$ exhibits real eigenvalues for 0<g<g_c$0<g<g_c$ and a PT phase transition at g_c$g_c$.     

On analogues of black brane solutions in the model with multicomponent anisotropic fluid

A family of spherically symmetric solutions with horizon in the model with m  -component anisotropic fluid is presented. The metrics are defined on a manifold that contains a product of n−1$n-1$ Ricci-flat “internal” spaces. The equation of state for any s  -th component is defined by a vector Us$U^s$ belonging to Rn+1${\mathbb{R}}^{n+1}$. The solutions are governed by moduli functions Hs$H_s$ obeying non-linear differential equations with certain boundary conditions imposed. A simulation of black brane solutions in the model with antisymmetric forms is considered. An example of solution imitating M₂–M₅$M_2\text{–}{M}_5$ configuration (in D=11$D=11$ supergravity) corresponding to Lie algebra A₂$A_2$ is presented.     

Non-Abelian fusion rules from an Abelian system

We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n$n$ dimensional vector space which we call H_n$H_n$. The Z_p${\mathbb{Z}}_p$ gauge particles act on the vertex particles and thus H_n$H_n$ can be thought of as a C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n$n$ and p$p$, though we believe this feature holds for all n>p$n>p$. We will see that non-Abelian anyons of the quantum double of C(S₃)$\mathbb{C}\left(S_3\right)$ are obtained as part of the vertex excitations of the model with n=6$n=6$ and p=3$p=3$. Ising anyons are obtained in the model with n=4$n=4$ and p=2$p=2$. The n=3$n=3$ and p=2$p=2$ case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Z_p${\mathbb{Z}}_p$. This makes them possible candidates for realizing quantum computation.