Gravity in spacetimes with cosmological constants

This thesis is composed of two parts: gravity in the spacetime with a negative/positive cosmological constant. The first part, which is the negative case, devotes to constructing the IIB supergravity dual solution in AdS/CFT correspondence for N = (1, 0) and N = (1/2, 0) non-anticommutative deformed super Yang-Mills theory. The non-anticommutativity is realised on N D3-branes in certain constant self-dual RR 5-form background fields. These background fields can be sourced by a set of additional D3-branes intersecting the N D3's. By taking the near horizon limit to the brane configurations, the supergravity solutions are obtained. The mapping between the bulk scalar fields and the boundary operators for N = (1, 0) case is investigated, and it is found that the spectrum of a particular class of the BPS operators is not deformed by the non-anticommutativity. The second part is for the positive cosmological constant case. In this part, a black fusiform solution with appositive cosmological const in d =5, N = 4 de Sitter supergravity is constructed. The solution is obtained via the braneworld Kaluza-Klein reduction ansatz, and preserves half of the de Sitter supersymmetry. It is static, with the gravitational contraction being balanced by the cosmological repulsion. The black fusiform has an event horizon and a cosmological horizon, and is asymptotically non-de Sitter. The horizons are of an in x S(^2) topology, and contain singularities at the opposite ends due to the nature of the reduction ansatz. Despite the singularities, the solution exhibits some physically properties compatible with that of the regular asymptotically de Sitter spacetimes. The entropy and mass observe the N-bound proposal and the maximal mass conjecture respectively. It also carries a charge which contributes to the 1st law of black hole mechanics

Spin chains and classical strings in rotating Rindler-AdS space

In this paper, we study the spin chain and string excitation in the rotating Rindler-$AdS_3$ proposed in [12]. We obtain a one-parameter deformed $SL(2)$ spin chain at the fast spin limit. Two-spin GKP-like solutions are studied at short and long string limits. General ansatz for the giant magnons and the spiky strings are analyzed in detail for various $\beta$. At last, we explore its counterpart in analytic continuation and pp-wave limit.Comment: 23pp, 8 figure

Engineering Holographic Superconductor Phase Diagrams

We study how to engineer holographic models with features of a high temperature superconductor phase diagram. We introduce a field in the bulk which provides a tunable "doping" parameter in the boundary theory. By designing how this field changes the effective masses of other order parameter fields, desired phase diagrams can be engineered. We give examples of generating phase diagrams with phase boundaries similar to a superconducting dome and an anti-ferromagnetic phase by including two order parameter fields. We also explore whether the pseudo gap phase can be described without adding another order parameter field and discuss the potential scaling symmetry associated with a quantum critical point hidden under the superconducting dome in this phase diagram.Comment: 25 pages, 7 figure

Towards Searching for Entangled Photons in the CMB Sky

We explore the possibility of detecting entangled photon pairs from cosmic microwave background or other cosmological sources coming from two patches of the sky. The measurements use two detectors with different photon polarizer directions. When two photon sources are separated by a large angle relative to the earth, such that each detector has only one photon source in its field of view, a null test of unentangled photons can be performed. The deviation from this unentangled background is, in principle, the signature of photon entanglement. To confirm whether the deviation is consistent with entangled photons, we derive a photon polarization correlation to compare with, similar to that in a Bell inequality measurement. However, since photon coincidence measurement cannot be used to discriminate unentangled cosmic photons, it is unlikely that the correlation expectation value alone can violate Bell inequality to provide the signature for entanglement.Comment: 5 pages, 2 figure; references added, typos fixed. v3 revised version with more discussions on detection possibilities; added references.v4 published version in PR

On Black Ring with a Positive Cosmological Constant

We consider black ring with a cosmological constant in the five dimensional N=4 de Sitter supergravity theory. Our solution preserves half of the de Sitter supersymmetries and has one rotation symmetry. Unlike the flat case, there is no angular momentum and the stability against gravitational self-attraction is balanced by the cosmological repulsion due to the cosmological constant. Our solution describes a singular black ring since although it has horizons of topology S^1 x S^2, the horizons are singular. Despite the singularity, our solution displays some interesting regular physical properties: it carries a dipole charge and this charge contributes to the first law of thermodynamics; it has an entropy and mass which conform to the entropic N-bound proposal and the maximal mass conjecture We conjecture that the Gregory-Laflamme instability leads to a resolution of the singularity and results in a regular black ring.Comment: v2. LaTex, 19 pages. with some corrections and comments adde

Dynamical Instability of Holographic QCD at Finite Density

In this paper we study the dynamical instability of Sakai-Sugimoto's holographic QCD model at finite baryon density. In this model, the baryon density, represented by the smeared instanton on the worldvolume of the probe D8-\overline{D8} mesonic brane, sources the worldvolume electric field, and through the Chern-Simons term it will induces the instability to form a chiral helical wave. This is similar to Deryagin-Grigoriev-Rubakov instability to form the chiral density wave for large N_c QCD at finite density. Our results show that this kind of instability occurs for sufficiently high baryon number densities. The phase diagram of holographic QCD will thus be changed from the one which is based only on thermodynamics. This holographic approach provides an effective way to study the phases of QCD at finite density, where the conventional perturbative QCD and lattice simulation fail.Comment: 18 pages, 6 figures;v2. add thermodynamics discussion; v4. Treatment of the instanton energy changed and QGP analysis added. Some figures replaced and added, including the phase diagra

Entanglement Entropy and Quantum Phase Transition in the O(N)O(N) σ\sigma-model

We investigate how entanglement entropy behaves in a system with a quantum phase transition. We study the $\sigma$-model which has an $O(N)$ symmetry when the mass squared parameter $\mu^2$ is positive, and when $\mu^2$ is negative, this symmetry is broken spontaneously. The area law and the leading divergence of entanglement entropy are preserved in both the symmetric and the broken phases. In 3+1 dimensions, the spontaneous symmetry breaking changes the subleading divergence from a log to log squared, while in 2+1 dimensions the subleading divergent structure is unchanged. At the leading order of the coupling constant expansion, the entanglement entropy reaches its local maximum with a cusp at the quantum phase transition point $\mu^2=0$ and decreases while $|\mu^2|$ is increased. We also find novel scaling behavior of the entanglement entropy near the transition point.Comment: 32 pp., 6 figures. v2. scaling behavior revised, 3 references added, submitted to JHE

Studies on modified limited-memory BFGS method in full waveform inversion

Full waveform inversion (FWI) is a non-linear optimization problem based on full-wavefield modeling to obtain quantitative information of subsurface structure by minimizing the difference between the observed seismic data and the predicted wavefield. The limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method is an effective quasi-Newton method in FWI due to its high inversion efficiency with low calculation and storage requirements. Like other conventional quasi-Newton methods, the approximation of the Hessian matrix in the L-BFGS method satisfies the quasi-Newton equation, which only exploits the gradient and model information while the available objective function value is neglected. The modified quasi-Newton equation considers the gradient, model, and objective function information together. Theoretical analysis reveals that the modified quasi-Newton equation is superior to the conventional quasi-Newton equation as it achieves higher-order accuracy in approximating the Hessian matrix. The modified L-BFGS method can be obtained by using the modified quasi-Newton equation to modify the L-BFGS method. This modification improves the accuracy of the Hessian matrix approximation with little increase of calculation for each iteration. We incorporate the modified L-BFGS method into FWI, numerical results show that the modified L-BFGS method has a higher convergence rate, achieves better inversion results, and has stronger anti-noise ability than the conventional L-BFGS method

Estimated Acute Effects of Ambient Ozone and Nitrogen Dioxide on Mortality in the Pearl River Delta of Southern China

Background and objectives: Epidemiologic studies have attributed adverse health effects to air pollution; however, controversy remains regarding the relationship between ambient oxidants [ozone (O3) and nitrogen dioxide (NO2)] and mortality, especially in Asia. We conducted a four-city time-series study to investigate acute effects of O3 and NO2 in the Pearl River Delta (PRD) of southern China, using data from 2006 through 2008