Holographic RG Flow in a New SO(3)×SO(3)SO(3)\times SO(3) Sector of ω\omega-Deformed SO(8)SO(8) Gauged N=8{\cal N}=8 Supergravity

We consider a certain ${\cal N}=1$ supersymmetric, $SO(3)\times SO(3)$ invariant, subsector of the $\omega$-deformed family of $SO(8)$-gauged ${\cal N}=8$ four-dimensional supergravities. The theory contains two scalar fields and two pseudoscalar fields. We look for stationary points of the scalar potential, corresponding to AdS vacua in the theory. One of these, which breaks all supersymmetries but is nonetheless stable, is new. It exists only when $\omega\ne 0$. We construct supersymmetric domain wall solutions in the truncated theory, and we give a detailed analysis of their holographic dual interpretations using the AdS/CFT correspondence. Domain walls where the pseudoscalars vanish were studied previously, but those with non-vanishing pseudoscalars, which we analyse numerically, are new. The pseudoscalars are associated with supersymmetric mass deformations in the CFT duals. When $\omega$ is zero, the solutions can be lifted to M-theory, where they approach the Coulomb-branch flows of dielectric M5-branes wrapped on $S^3$ in the deep IR.Comment: 40 pages, 10 figure

An in-host model of HIV incorporating latent infection and viral mutation

We construct a seven-component model of the in-host dynamics of the Human Immunodeficiency Virus Type-1 (i.e, HIV) that accounts for latent infection and the propensity of viral mutation. A dynamical analysis is conducted and a theorem is presented which characterizes the long time behavior of the model. Finally, we study the effects of an antiretroviral drug and treatment implications.Comment: 10 pages, 7 figures, Proceedings of AIMS Conference on Differential Equations and Dynamical Systems (2015

Three-Dimensional Topological Insulator in a Magnetic Field: Chiral Side Surface States and Quantized Hall Conductance

Low energy excitation of surface states of a three-dimensional topological insulator (3DTI) can be described by Dirac fermions. By using a tight-binding model, the transport properties of the surface states in a uniform magnetic field is investigated. It is found that chiral surface states parallel to the magnetic field are responsible to the quantized Hall (QH) conductance $(2n+1)\frac{e^2}{h}$ multiplied by the number of Dirac cones. Due to the two-dimension (2D) nature of the surface states, the robustness of the QH conductance against impurity scattering is determined by the oddness and evenness of the Dirac cone number. An experimental setup for transport measurement is proposed

A direct calculation of critical exponents of two-dimensional anisotropic Ising model

Using an exact solution of the one-dimensional (1D) quantum transverse-field Ising model (TFIM), we calculate the critical exponents of the two-dimensional (2D) anisotropic classical Ising model (IM). We verify that the exponents are the same as those of isotropic classical IM. Our approach provides an alternative means of obtaining and verifying these well-known results.Comment: 3 pages, no figures, accepted by Commun. Theor. Phys.(IPCAS

Critical Behavior in the Rotating D-branes

The low energy excitation of the rotating D3-branes is thermodynamically stable up to a critical angular momentum density. This indicates that there is a corresponding phase transition of the ${\cal N}$=4 large $N$ super Yang-Mills theory at finite temperature. On the side of supergravity, we investigate the phase transition in the grand canonical ensemble and canonical ensemble. Some critical exponents of thermodynamic quantities are calculated. They obey the static scaling laws. Using the scaling laws related to the correlation length, we get the critical exponents of the correlation function of gauge field. The thermodynamic stability of low energy excitations of the rotating M5-branes and rotating M2-branes is also studied and similar critical behavior is observed. We find that the critical point is shifted in the different ensembles and there is no critical point in the canonical ensemble for the rotating M2-branes. We also discuss the Hawking-Page transition for these rotating branes. In the grand canonical ensemble, the Hawking-Page transition does not occur. In the canonical ensemble, however, the Hawking-Page transition may appear for the rotating D3- and M5-branes, but not for the rotating M2-branes.Comment: Revtex, 17 pages, minor changes, the discussion on the Hawking-Page transition and references adde