Holographic quark-antiquark potential in hot, anisotropic Yang-Mills plasma
Using the gauge/gravity duality we calculate the heavy quark–antiquark potential in a hot, anisotropic and strongly coupled Yang–Mills plasma in ( 3 + 1 )-dimensions. As the anisotropic medium we take a deformed version of N = 4 super Yang–Mills theory at finite temperature following a recent work where the dual type IIB supergravity solution is also proposed. We turn on a small value of the anisotropy parameter, for which the gravity dual is known analytically (perturbatively), and compute the velocity-dependent quark–antiquark interaction potential when the pair is moving through the plasma with a velocity v . By setting v = 0 we recover the static quark–antiquark potential. We numerically study how the potential is modified in the presence of anisotropy. We further show numerically how the quark–antiquark separation (both in the static and the velocity-dependent case) and hence, the screening length gets modified by anisotropy. We discuss various cases depending upon the direction of the dipole and the direction of its propagation and make a comparative study of these cases. We are also able to obtain an analytical expression for the screening length of the dipole moving in a hot, anisotropic plasma in a special case.

title: Calculating the jet quenching parameter in the plasma of NCYM theory from gauge/gravity duality
abstract: A particular decoupling limit of the nonextremal (D1, D3) brane bound state system of type IIB string theory is known to give the gravity dual of space-space noncommutative Yang-Mills theory at finite temperature. We use a string probe in this background to compute the jet quenching parameter in a strongly coupled plasma of hot noncommutative Yang-Mills theory in ($3+1$) dimensions from gauge/gravity duality. We give expressions for the jet quenching parameter for both small and large noncommutativity. For small noncommutativity, we find that the value of the jet quenching parameter gets reduced from its commutative value. The reduction is enhanced with temperature as ${T}^{7}$ for fixed noncommutativity and fixed 't Hooft coupling. We also give an estimate of the correction due to noncommutativity at the present collider energies like in RHIC or in LHC and find it too small to be detected. We further generalize the results for noncommutative Yang-Mills theories in diverse dimensions.

title: An eigenvalue problem in two dimensions for an irregular boundary
abstract: An analytical perturbative method is suggested for solving the Helmholtz equation (∇2 + k2)ψ = 0 in two dimensions where ψ vanishes on an irregular closed curve. We can thus find the energy levels of a quantum mechanical particle confined in an infinitely deep potential well in two dimensions having an irregular boundary or the vibration frequencies of a membrane whose edge is an irregular closed curve. The method is tested by calculating the energy levels for an elliptical and a supercircular boundary and comparing with the results obtained numerically. Further, the phenomenon of level crossing due to shape variation is also discussed.

title: Wilson loops in (p+1)-dimensional Yang–Mills theories using gravity/gauge theory correspondence
abstract: We compute the expectation values of both the time-like and the light-like Wilson loops in a strongly coupled plasma of ( p + 1 ) -dimensional Yang–Mills theories using gravity/gauge theory correspondence. From the time-like Wilson loop we obtain the velocity dependent quark–antiquark potential where the dipole is moving through the plasma with an arbitrary velocity 0 v 1 and also obtain expressions for the screening lengths. When the velocity v → 1 , the Wilson loop becomes light-like and we obtain the form of the jet quenching parameter in those strongly coupled plasma.

title: Role of symmetry potential in nuclear symmetry energy and its density slope parameter
abstract: Using a density dependent finite-range effective interaction of Yukawa form the nuclear mean field in asymmetric nuclear matter is expanded in terms of power series of asymmetry β ( = ρ n − ρ p ρ ) as u τ ( k , ρ , β ) = u 0 ( k , ρ ) ± u sym , 1 ( k , ρ ) β + u sym , 2 ( ρ ) β 2 . The behavior of nuclear symmetry potential u sym , 1 ( k , ρ ) around the Fermi momentum k f is found to be connected to the density dependence of symmetry energy E sym ( ρ ) and nucleon effective mass m 0 ⁎ m ( k = k f , ρ ) in symmetric nuclear matter. Two different trends of momentum dependence for nuclear symmetry potential is observed depending on the choice of strength parameters of exchange interaction, but at Fermi momentum it is found to be independent of the choice of parameters. The nuclear symmetry energy E sym ( ρ ) and its slope L ( ρ ) are expressed analytically in terms of nuclear mean field in isospin asymmetric nuclear matter using the same interaction. We find that the second order nuclear symmetry potential u sym , 2 ( ρ ) cannot be neglected while calculating the density slope of symmetry energy L ( ρ ) as well as the nuclear mean field in extremely neutron (proton) rich nuclear matter.

title: A New Result on the Dynamical Symmetry of Spherical Collapse
abstract: A dynamical symmetry for spherical collapse has been studied using a linear transformation of the initial data set (mass and kinetic energy function) and the area radius. With proper choice of the initial area radius, the evolution as well as the physical parameters namely energy density and shear remain invariant both initially and at any time instant. Finally, it is found that the final outcome of collapse depends on the initial choice of the area radius.

title: Spherically Symmetric Vacuum Brane and Wormhole Solutions
abstract: In this letter, we have obtained static, spherically symmetric solutions of the effective vacuum Einstein field equations on a brane embedded in a five dimensional space time. The effective stress tensor is induced by the interaction with the bulk gravitational field and is given by the electric part of the five dimensional Weyl tensor. Due to traceless nature of this non-local effect of the bulk, any solution of  (4)R=0 is a possible solution of the vacuum brane. We have derived a class of solutions, which corresponds to wormhole solution. Physical properties and characteristics of the wormhole are studied.

title: Non-standard interaction in neutrino oscillations and recent Daya Bay, T2K experiments
abstract: We study the possible constraints on non-standard interaction(NSIs) in a model independent way by considering the recent results from T2K and Daya Bay neutrino oscillations experiments. Using perturbation method we present generic formulas (suitable for T2K baseline and for large $\theta_{13}$ as evident from Daya Bay) for the probability of oscillation for $\nu_\mu \rightarrow \nu_e$, taking into account NSIs at source ($\epsilon^s$), detector ($\epsilon^d$) and during propagation ($\epsilon^m$) of neutrinos through matter. Two separate cases of perturbation with small (slightly large) NSI ($\epsilon_{\alpha\beta}^m \sim 0.03(0.18)$) are discussed in detail. Using various possible presently allowed NSI values we reanalyze numerically the $\theta_{13} - \delta$ allowed region given by recent T2K experimental data. We obtain model independent constraints on NSIs in the $\delta-\epsilon_{\alpha\beta}^m$ plane using the $\theta_{13}$ value as measured by Daya Bay, where $\delta$ is the CP violating phase. Depending on $\delta$ values significant constraints on $\epsilon_{e\tau}$ and $\epsilon_{\tau\tau}$, in particular, are possible for both hierarchies of neutrino masses. Corresponding to T2K's 66% confidence level result, the constraints on $\epsilon_{\tau\tau}$ is shown to be independent of any $\delta$ value.

title: Shell Crossing Singularities in Quasi-Spherical Szekeres Models
abstract: In the study of gravitational collapse, we always encounter with two types of singularities − shell focusing singularity and shell crossing singularity. In Tolman-Bondi-Lemâıtre (TBL) dust model, these two kinds of singularities will corresponds to R = 0 and R = 0 respectively. A shell focusing singularity (i.e., R = 0) on a shell of dust occurs when it collapses at or starts expanding from the centre of matter distribution. The instant at which a shell at the radial co-ordinate r will reach the centre of the matter distribution should be a function of r. So different shells of dust arrive at the centre at different times and there is always a possibility that any two shells of dust cross each other at a finite radius in course of their collapse. In this situation the comoving system breaks down, both the matter density and kretchmann scalar diverge [1,2] and one encounters the shell crossing singularity. If one treats it as the boundary surface then the region beyond it is unacceptable since it has negative density. It is therefore, of interest to find conditions which guarantee that no shell crossing will occur.