Refined Topological Vertex and Instanton Counting

It has been proposed recently that topological A-model string amplitudes for toric Calabi-Yau 3-folds in non self-dual graviphoton background can be caluculated by a diagrammatic method that is called the ``refined topological vertex''. We compute the extended A-model amplitudes for SU(N)-geometries using the proposed vertex. If the refined topological vertex is valid, these computations should give rise to the Nekrasov's partition functions of N=2 SU(N) gauge theories via the geometric engineering. In this article, we verify the proposal by confirming the equivalence between the refined A-model amplitude and the K-theoretic version of the Nekrasov's partition function by explicit computation.Comment: 22 pages, 6 figures, minor correction

Parametric derivation of the observable relativistic periastron advance for binary pulsars

We compute the dimensionless relativistic periastron advance parameter $k$, which is measurable from the timing of relativistic binary pulsars. We employ for the computation the recently derived Keplerian-type parametric solution to the post-Newtonian (PN) accurate conservative dynamics of spinning compact binaries moving in eccentric orbits. The parametric solution and hence the parameter $k$ are applicable for the cases of \emph{simple precession}, namely, case (i), the binary consists of equal mass compact objects, having two arbitrary spins, and case (ii), the binary consists of compact objects of arbitrary mass, where only one of them is spinning with an arbitrary spin. Our expression, for the cases considered, is in agreement with a more general formula for the 2PN accurate $k$, relevant for the relativistic double pulsar PSR J0737--3039, derived by Damour and Sch\"afer many years ago, using a different procedure.Comment: 12 pages including 1 figure; submitted to PR

(De)Constructing Dimensions

We construct renormalizable, asymptotically free, four dimensional gauge theories that dynamically generate a fifth dimension.Comment: 10 pages, late

From Matrices to Strings and Back

We discuss an explicit construction of a string dual for the Gaussian matrix model. Starting from the matrix model and employing Strebel differential techniques we deduce hints about the structure of the dual string. Next, following these hints a worldheet theory is constructed. The correlators in this string theory are assumed to localize on a finite set of points in the moduli space of Riemann surfaces. To each such point one associates a Feynman diagram contributing to the correlator in the dual matrix model, and thus recasts the worldsheet expression as a sum over Feynman diagrams.Comment: 27 pages, 3 figure

Discrete Wavelet Transform based Cryptosystem

In this article, the authors proposed, implemented and analysed a symmetric key cryptographic algorithm that can be considered as a lossless encryption and decryption technique, advantageous especially in situations where, even a slight marginal distortion is not tolerable. In the proposed system, Haar wavelet is used initially, to transform the original target image into its frequency domain, followed by  encrypting the resulting sub-bands, so as to obtain a secure and reliable encrypted image. The resulting coefficients after Haar decomposition is scattered using a reversible weighing factor, suitably reversed and swapped to get the secure encrypted image. The encrypted image is  then correspondingly decrypted, by the reverse process to get back the original decrypted image. Statistical testing and security methods were used to evaluate and analyse the proposed cryptosystem and the results showed that the proposed system is cryptographically resistant to attacks and is also highly secure when compared to other cryptographic systems in the frequency domain

Phasing of gravitational waves from inspiralling eccentric binaries at the third-and-a-half post-Newtonian order

We obtain an efficient description for the dynamics of nonspinning compact binaries moving in inspiralling eccentric orbits to implement the phasing of gravitational waves from such binaries at the 3.5 post-Newtonian (PN) order. Our computation heavily depends on the phasing formalism, presented in [T. Damour, A. Gopakumar, and B. R. Iyer, Phys. Rev. D \textbf{70}, 064028 (2004)], and the 3PN accurate generalized quasi-Keplerian parametric solution to the conservative dynamics of nonspinning compact binaries moving in eccentric orbits, available in [R.-M. Memmesheimer, A. Gopakumar, and G. Sch\"afer, Phys. Rev. D \textbf{70}, 104011 (2004)]. The gravitational-wave (GW) polarizations $h_{+}$ and $h_{\times}$ with 3.5PN accurate phasing should be useful for the earth-based GW interferometers, current and advanced, if they plan to search for gravitational waves from inspiralling eccentric binaries. Our results will be required to do \emph{astrophysics} with the proposed space-based GW interferometers like LISA, BBO, and DECIGO.Comment: 22 pages including 2 figures; submitted to PR

't Hooft Expansion of 1/2 BPS Wilson Loop

We revisit the 't Hooft expansion of 1/2 BPS circular Wilson loop in N=4 SYM studied by Drukker and Gross in hep-th/0010274. We find an interesting recursion relation which relates different number of holes on the worldsheet. We also argue that we can turn on the string coupling by applying a certain integral transformation to the planar result.Comment: 21 pages; v2: minor correction