Propagation of generalized vector Helmholtz-Gauss beams through paraxial optical systems

We introduce the generalized vector Helmholtz-Gauss (gVHzG) beams that constitute a general family of localized beam solutions of the Maxwell equations in the paraxial domain. The propagation of the electromagnetic components through axisymmetric ABCD optical systems is expressed elegantly in a coordinate-free and closed-form expression that is fully characterized by the transformation of two independent complex beam parameters. The transverse mathematical structure of the gVHzG beams is form-invariant under paraxial transformations. Any paraxial beam with the same waist size and transverse spatial frequency can be expressed as a superposition of gVHzG beams with the appropriate weight factors. This formalism can be straightforwardly applied to propagate vector Bessel-Gauss, Mathieu-Gauss, and Parabolic-Gauss beams, among others

Propagation dynamics of vector Mathieu-Gauss beams

The vector Mathieu-Gauss beams of integer order are examined as the solutions of the vector paraxial wave equation in elliptical coordinates. The propagation of the vector components and the three-dimensional intensity distribution of focused vector Mathieu-Gauss beams are analyzed for a variety of polarizations. Conditions in which the linearly polarized Mathieu-Gauss beams can be approximated by the scalar solutions of the paraxial wave equation are also discussed

M-Theory in the Gaugeon Formalism

In this paper we will analyse the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory in $\mathcal{N}=1$ superspace formalism. We then study the quantum gauge transformations for this ABJM theory in gaugeon formalism. We will also analyse the extended BRST symmetry for this ABJM theory in gaugeon formalism and show that these BRST transformations for this theory are nilpotent and this in turn leads to the unitary evolution of the $\mathcal{S}$-matrix.Comment: 8 pages, 0 figures, accepted for publication in Comm. Theor. Phy

Kaluza-Klein gauge and minimal integrable extension of OSp(4|6)/(SO(1,3) x U(3)) sigma-model

Basing upon experience from performing double-dimensional reduction of the D=11 supermembrane on AdS_4 x S^7 background to Type IIA superstring on AdS_4 x CP^3 we introduce Kaluza-Klein (partial) kappa-symmetry gauge as a vanishing condition of the contribution to the D=11 supervielbein components tangent to D=10 space-time proportional to the differential of the coordinate parametrizing compact 11-th space-time dimension, that is identified with the supermembrane world-volume compact dimension. For AdS_4 x S^7 supermembrane Kaluza-Klein gauge removes half Grassmann coordinates associated with 8 space-time supersymmetries, broken by the AdS_4 x CP^3 superbackground, by imposing D=3 (anti-)Majorana condition on them. The consideration relies on the realization of osp(4|8) isometry superalgebra of the AdS_4 x S^7 superbackground as D=3 N=8 superconformal algebra. Requiring further vanishing of the D=10 dilaton leaves in the sector of broken supersymmetries just two Grassmann coordinates organized into D=3 (anti-)Majorana spinor that defines minimal SL(2,R)-covariant extension of the OSp(4|6)/(SO(1,3)x U(3)) sigma-model. Among 4 possibilities of such a minimal extension we consider in detail one, that corresponds to picking out D=3 Majorana coordinate related to broken Poincare supersymmetry, and show that the AdS_4 x CP^3 superstring equations of motion in this partial kappa-symmetry gauge are integrable. Also the relation between the OSp(4|6)/(SO(1,3) x U(3)) sigma-model and the AdS_4 x CP^3 superstring is revisited.Comment: LaTeX, 22 pages; v2: minor improvements in the text, typos corrected, references adde

Mass Deformation of the Multiple M2 Branes Theory

Based on recent developments, in this letter we study the one parameter deformation of 2+1 dimensional gauge theories with scale invariance and N = 8 supersymmetry, which is expected to be the field theory living on a stack of M2 branes. The deformed gauge theory is defined by a Lagrangian and is based on an infinite set of novel 3-algebras constructed by relaxing the assumption that the invariant metric is positive definite. Under the Higgs mechanism, we can obtain the D-branes world volume theory in the presence of background fluxes.Comment: 13pages, no figures, reference adde

Eliminating ambiguities for quantum corrections to strings moving in AdS4×CP3AdS_4\times \mathbb{CP}^3

We apply a physical principle, previously used to eliminate ambiguities in quantum corrections to the 2 dimensional kink, to the case of spinning strings moving in $AdS_4\times \mathbb{CP}^3$, thought of as another kind of two dimensional soliton. We find that this eliminates the ambiguities and selects the result compatible with AdS/CFT, providing a solid foundation for one of the previous calculations, which found agreement. The method can be applied to other classical string "solitons".Comment: 18 pages, latex; references added, comments added at end of section 4, a few words changed; footnote added on page 1

Nambu-Poisson Bracket and M-Theory Branes Coupled to Antisymmetric Fluxes

By using the recently proposed prescription arXiv:0804.3629 for obtaining the $M5$ brane action from multiple $M2$ branes action in BLG theory, we examine such transition when 11 Dimensional background antisymmetric fluxes couple to the $M2$ brane world volume. Such couplings was suggested in arXiv:0805.3427 where it was used the fact that various fields in BLG theory are valued in a Lie 3-algebra. We argue that this action and promoting it by Nambu-Poisson bracket gives the expected coupling of fluxes with $M5$ brane at least at weak coupling limit. We also study some other aspects of the action for example, the gauge invariance of the theory.Comment: 14 page

Three-dimensional N=8 conformal supergravity and its coupling to BLG M2-branes

This paper is concerned with the problem of coupling the N=8 superconformal Bagger-Lambert-Gustavsson (BLG) theory to N=8 conformal supergravity in three dimensions. We start by constructing the on-shell N=8 conformal supergravity in three dimensions consisting of a Chern-Simons type term for each of the gauge fields: the spin connection, the SO(8) R-symmetry gauge field and the spin 3/2 Rarita-Schwinger (gravitino) field. We then proceed to couple this theory to the BLG theory. The final theory should have the same physical content, i.e., degrees of freedom, as the ordinary BLG theory. We discuss briefly the properties of this "topologically gauged" BLG theory and why this theory may be useful.Comment: 20 pages, v2: references and comments added, presentation in section 3.2 extended. v3: misprints and a sign error corrected, version published in JHE

Combining chemotherapy and targeted therapies in metastatic colorectal cancer

Colorectal cancer remains one of the major causes of cancer death worldwide. During the past years, the development of new effective treatment options has led to a considerable improvement in the outcome of this disease. The advent of agents such as capecitabine, irinotecan, oxaliplatin, cetuximab and bevacizumab has translated into median survival times in the range of 2 years. Intense efforts have focused on identifying novel agents targeting specific growth factor receptors, critical signal transduction pathways or mediators of angiogenesis. In addition, several clinical trials have suggested that some of these molecularly targeted drugs can be safely and effectively used in combination with conventional chemotherapy. In this article we review various treatment options combining cytotoxic and targeted therapies currently available for patients with metastatic colorectal cancer