Abstract:
We recently proposed an empirical approach for the Landau-Pomeranchuk-Migdal (LPM) effects in photon emission from the quark gluon plasma as a function of photon mass. This approach was based on Generalized Emission Functions (GEF) for photon emission, derived at a fixed temperature and strong coupling constant. In the present work, we have extended the LPM calculations for several temperatures and strong coupling strengths. The integral equations for (${\bf \tilde{f}(\tilde{p}_\perp)}$) and ($\tilde{g}({\bf \tilde{p}_\perp})$) are solved by the iterations method for the variable set \{$p_0,q_0,Q^2,T,\alpha_s$\}, considering bremsstrahlung and $\bf aws$ processes. We generalize the dynamical scaling variables, $x_T$, $x_L$, for bremsstrahlung and {\bf aws} processes which are now functions of variables $p_0,q_0,Q^2,T,\alpha_s$. The GEF introduced earlier, $g^b_T$, $g^a_T$, $g^b_L$, $g^a_L$, are also generalized for any temperatures and coupling strengths. From this, the imaginary part of the photon polarization tensor as a function of photon mass and energy can be calculated as a one dimensional integral over these GEF and parton distribution functions in the plasma. However, for phenomenological studies of experimental data, one needs a simple empirical formula without involving parton momentum integrations. Therefore, we present a phenomenological formula for imaginary photon polarization tensor as a function of \{$q_0,Q^2,T,\alpha_s$\} that includes bremsstrahlung and $\bf aws$ mechanisms along with LPM effects.

Abstract:
We describe a supersymmetric example of the holographic duality between 3 dimensional vector models and higher spin gauge theories in AdS_4, first proposed in a bosonic context by Klebanov and Polyakov. We argue that a particular Fradkin-Vasiliev type supersymmetric higher spin gauge theory in AdS_4 with 16 supersymmetries is dual to the singlet sector of bilinear operators of a free N = 4, SU(N) vector model defined on the boundary. Starting from the duality between type IIB on AdS_5 \times S^5 with a D5-brane as an AdS_4 \times S^2 subspace and the 4 dimensional SU(N) SYM with a defect, we recover the duality between our vector model and the higher spin gauge theory. In this case, we propose that the higher spin gauge theory is a truncation of the open string theory on the world volume of the D5-brane in its tensionless string limit. We also comment on a possible Higgs mechanism in our model.

Abstract:
Gluon radiation is an important mechanism for parton energy loss as the parton traverses the quark gluon plasma (QGP) medium. We studied the gluon emission in QGP using AMY formalism. In the present work, we obtained gluon emission amplitude {\bf F}({\bf h},p,k) function, which is a solution of the integral equations describing gluon radiation including Landau-Pomeranchuk-Migdal (LPM) effects, using iterations method. We define a new dynamical scale for gluon emission denoted by $x$. The gluon emission rate is obtained by integrating these amplitude function over {\bf h}. We show that these obey a simple scaling in terms of this dynamical variable $x$. We define the gluon emission function $g(x)$ for gluon radiation for the three processes $g\rightarrow gg$, $q\rightarrow gq$ and $g\rightarrow q\bar{q}$. In terms of this $g(x)$ function, the parton energy loss calculations, due to medium induced gluon radiation, may become simplified.

Abstract:
We consider the n^{th} order nonlinear differential equation on time scales

subject to the right focal type two-point boundary conditions

We establish a criterion for the existence of at least one positive solution by utilizing Krasnosel’skii fixed point theorem. And then, we establish the existence of at least three positive solutions by utilizing Leggett-Williams fixed point theorem.

Abstract:
We describe a tachyon-free stable non-BPS brane configuration in type IIA string theory. The configuration is an elliptic model involving rotated NS5 branes, D4 branes and anti-D4 branes, and is dual to a fractional brane-antibrane pair placed at a conifold singularity. This configuration exhibits an interesting behaviour as we vary the radius of the compact direction. Below a critical radius the D4 and anti-D4 branes are aligned, but as the radius increases above the critical value the potential between them develops a minimum away from zero. This signals a phase transition to a configuration with finitely separated branes.

Abstract:
In the limit of large, constant B-field (the ``Seiberg-Witten limit''), the derivative expansion for open-superstring effective actions is naturally expressed in terms of the symmetric products *n. Here, we investigate corrections around the large-B limit, for Chern-Simons couplings on the brane and to quadratic order in gauge fields. We perform a boundary-state computation in the commutative theory, and compare it with the corresponding computation on the noncommutative side. These results are then used to examine the possible role of Wilson lines beyond the Seiberg-Witten limit. To quadratic order in fields, the entire tree-level amplitude is described by a metric-dependent deformation of the *2 product, which can be interpreted in terms of a deformed (non-associative) version of the Moyal * product.

Abstract:
We study orientifolds of type IIB string theory in the plane-wave background supported by null RR 3-form flux F^{(3)}. We describe how to extract the RR tadpoles in the Green-Schwarz formalism in a general setting. Two models with orientifold groups {1, \Omega} and {1,\Omega I_4}, which are T-dual to each other, are considered. Consistency of these backgrounds requires 32 D9 branes for the first model and 32 D5 branes for the second one. We study the spectra and comment on the heterotic duals of our models.

Abstract:
Stable non-BPS states can be constructed and studied in a variety of contexts in string theory. Here we review some interesting constructions that arise from suspended and wrapped branes. We also exhibit some stable non-BPS states that have holographic duals.

Abstract:
We obtain the couplings of noncommutative branes of type II string theories to constant Ramond-Ramond backgrounds, for BPS as well as non-BPS branes, in the background-independent description. For the BPS branes, we also generalize these couplings to other descriptions, and thereby argue their equivalence to the known couplings in the commutative description. The first part is a review of earlier work while the second part contains some additional observations.

Abstract:
We examine string-theory orientifold planes of various types including the Sp and SO-odd planes, and deduce the gravitational Chern-Simons couplings on their world-volumes. Consistency checks are carried out in different spacetime dimensions using various dualities, including those relating string theory with F-theory and M-theory. It is shown that when an orientifold 3-plane crosses a 5-brane, the jump in the charge is accompanied by a corresponding change in the gravitational couplings.