Wess-Zumino-Witten Model for Galilean Conformal Algebra
In this note, we construct a Wess–Zumino–Witten model based on the Galilean conformal algebra in two-spacetime dimensions, which is a nonrelativistic analogue of the relativistic conformal algebra. We obtain exact background corresponding to σ-models in six dimensions (the dimension of the group manifold) and a central charge c = 6. We carry out a Sugawara type construction to verify the conformal invariance of the model. Further, we discuss the feasibility of the background obtained as a physical spacetime metric.

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: Holographic quark-antiquark potential in hot, anisotropic Yang-Mills plasma
abstract: 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: Eigenvalue problem in two dimensions for an irregular boundary: Neumann condition
abstract: We formulate a systematic elegant perturbative scheme for determining the eigenvalues of the Helmholtz equation (∇2 + k2)$ \psi$ = 0 in two dimensions when the normal derivative of $ \psi$ vanishes on an irregular closed curve. The unique feature of this method, unlike other perturbation schemes, is that it does not require a separate formalism to treat degeneracies. Degenerate states are handled equally elegantly as the non-degenerate ones. A real parameter, extracted from the parameters defining the irregular boundary, serves as a perturbation parameter in this scheme as opposed to earlier schemes where the perturbation parameter is an artificial one. The efficacy of the proposed scheme is gauged by calculating the eigenvalues for elliptical and supercircular boundaries and comparing with the results obtained numerically. We also present a simple and interesting semi-empirical formula, determining the eigenspectrum of the 2D Helmholtz equation with the Dirichlet or the Neumann condition for a supercircular boundary. A comparison of the eigenspectrum for several low-lying modes obtained by employing the formula with the corresponding numerical estimates shows good agreement for a wide range of the supercircular exponent.

title: Brownian motion in strongly coupled, anisotropic Yang-Mills plasma: A holographic approach
abstract: We employ methods of gauge/string duality to analyze the Brownian motion and the concomitant Langevin equation of a heavy quark in a strongly coupled, thermal, anisotropic Yang-Mills plasma. We consider fluctuations both along and perpendicular to the direction of anisotropy and study the effects of anisotropy on the drag coefficient, the diffusion constant and the Langevin coefficient for both the directions. We also verify the fluctuation-dissipation theorem for Brownian motion in an anisotropic medium.

title: INFLATIONARY SCENARIO IN BRANS–DICKE THEORY FOR BIANCHI VI0 SPACE–TIME MODEL
abstract: We have investigated perfect fluid model in Brans–Dicke theory for Bianchi VI0 space–time and have obtained exact analytical solutions considering barotropic equation of state. These solutions have been analyzed for different values of the parameters involved and some of them have shown a period of exponential expansion.

title: Dilatonic Scalar Field: A Dynamical System Analysis
abstract: The work deals with homogeneous and isotropic, flat FRW model of the universe which is filled up with non-interacting dark matter and dark energy to compatible with recent observational evidences. By choosing the dark energy in the form of a dilatonic scalar field, the evolution equations are reduced to an autonomous system. A phase space analysis is done around the critical points and stability criteria is examined. Finally, cosmological implications of the nature of the critical points are discussed.

title: The generalized second law of thermodynamics and the nature of the entropy function
abstract: In black-hole physics, the second law of thermodynamics is generally valid whether the black hole is a static or a non-static one. Considering the universe as a thermodynamical system the second law of black-hole dynamics extends to the non-negativity of the sum of the entropy of the matter and the horizon, known as generalized second law of thermodynamics (GSLT). Here, we have assumed the universe to be bounded by the event horizon where Bekenstein entropy-area relation and Hawking-temperature are not applicable. Thus considering entropy to be an arbitrary function of the area of the event horizon, we have tried to find the nature of the entropy function for the validity of the GSLT both in the quintessence era and in the phantom era. Finally, some graphical representation of the entropy function has been presented.

title: Motion of test particles around global monopoles in Brans-Dicke theory
abstract: A detailed analysis of the motion of test particles around global monopole in Brans-Dicke theory of gravity has been prescribed using the Hamilton-Jacobi (H-J) formalism. The trajectory of the test particles are trapped by the monopole with some restriction on the coupling parameter ω.

title: Liouville Type Dilatonic Potential in Locally Rotationally Symmetric Bianchi I Model
abstract: Exact solutions are obtained for a special case of locally rotationally symmetric Bianchi I models consisting of a dilaton scalar field and a Liouville type dilatonic potential interacting with an electromagnetic field coupled with gravity, and the corresponding properties of the space-time are discussed.