O(d,d)O(d,d)-Covariant String Cosmology

The recently discovered $O(d,d)$ symmetry of the space of slowly varying cosmological string vacua in $d+1$ dimensions is shown to be preserved in the presence of bulk string matter. The existence of $O(d,d)$ conserved currents allows all the equations of string cosmology to be reduced to first-order differential equations. The perfect-fluid approximation is not $O(d,d)$-invariant, implying that stringy fluids possess in general a non-vanishing viscosity.Comment: 13 page

O(d,d)-Duality in String Theory

A new method for obtaining dual string theory backgrounds is presented. Preservation of the Hamiltonian density and the energy momentum tensor induced by O(d,d)-transformations leads to a relation between dual sets of coordinate one-forms accompanied by a redefinition of the background fields and a shift of the dilaton. The necessity of isometric directions arises as integrability condition for this map. The isometry algebra is studied in detail using generalised geometry. In particular, non-abelian dualities and beta-transformations are contained in this approach. The latter are exemplified by the construction of a new approximate non-geometric background.Comment: 19+5 pages; v2: minor corrections and references added; v3: comments and references adde

A worldsheet extension of O(d,d;Z)

We study superconformal interfaces between N=(1,1) supersymmetric sigma models on tori, which preserve a u(1)^{2d} current algebra. Their fusion is non-singular and, using parallel transport on CFT deformation space, it can be reduced to fusion of defect lines in a single torus model. We show that the latter is described by a semi-group extension of O(d,d;Q), and that (on the level of Ramond charges) fusion of interfaces agrees with composition of associated geometric integral transformations. This generalizes the well-known fact that T-duality can be geometrically represented by Fourier-Mukai transformations. Interestingly, we find that the topological interfaces between torus models form the same semi-group upon fusion. We argue that this semi-group of orbifold equivalences can be regarded as the \alpha' deformation of the continuous O(d,d) symmetry of classical supergravity.Comment: 71 pages, 1 figure, minor additions and correction

O(D,D)\mathbf{O}(D,D) completion of the Friedmann equations

In string theory the closed-string massless NS-NS sector forms a multiplet of $\mathbf{O}(D,D)$ symmetry. This suggests a specific modification to General Relativity in which the entire NS-NS sector is promoted to stringy graviton fields. Imposing off-shell $\mathbf{O}(D,D)$ symmetry fixes the correct couplings to other matter fields and the Einstein field equations are enriched to comprise $D^{2}+1$ components, dubbed recently as the Einstein Double Field Equations. Here we explore the cosmological implications of this framework. We derive the most general homogeneous and isotropic ansatzes for both stringy graviton fields and the $\mathbf{O}(D,D)$-covariant energy-momentum tensor. Crucially, the former admits space-filling magnetic $H$-flux. Substituting them into the Einstein Double Field Equations, we obtain the $\mathbf{O}(D,D)$ completion of the Friedmann equations along with a generalized continuity equation. We discuss how solutions in this framework may be characterized by two equation-of-state parameters, $w$ and $\lambda$, where the latter characterizes the relative intensities of scalar and tensor forces. When $\lambda+3w=1$, the dilaton remains constant throughout the cosmological evolution, and one recovers the standard Friedmann equations for generic matter content (i.e. for any $w$). We further point out that, in contrast to General Relativity, neither an $\mathbf{O}(D,D)$-symmetric cosmological constant nor a scalar field with positive energy density gives rise to a de Sitter solution.Comment: v2: 31 + 13 pages; 1 figure. References added; abstract amended; discussion amended and clarified throughout. Results unchanged. To be published in EPJC. v1: 28 + 12 pages (main body + title, appendix, and references); 1 figur

A HOLISTIC REDUNDANCY- AND INCENTIVE-BASED FRAMEWORK TO IMPROVE CONTENT AVAILABILITY IN PEER-TO-PEER NETWORKS

Peer-to-Peer (P2P) technology has emerged as an important alternative to the traditional client-server communication paradigm to build large-scale distributed systems. P2P enables the creation, dissemination and access to information at low cost and without the need of dedicated coordinating entities. However, existing P2P systems fail to provide high-levels of content availability, which limit their applicability and adoption. This dissertation takes a holistic approach to device mechanisms to improve content availability in large-scale P2P systems. Content availability in P2P can be impacted by hardware failures and churn. Hardware failures, in the form of disk or node failures, render information inaccessible. Churn, an inherent property of P2P, is the collective effect of the users’ uncoordinated behavior, which occurs when a large percentage of nodes join and leave frequently. Such a behavior reduces content availability significantly. Mitigating the combined effect of hardware failures and churn on content availability in P2P requires new and innovative solutions that go beyond those applied in existing distributed systems. To addresses this challenge, the thesis proposes two complementary, low cost mechanisms, whereby nodes self-organize to overcome failures and improve content availability. The first mechanism is a low complexity and highly flexible hybrid redundancy scheme, referred to as Proactive Repair (PR). The second mechanism is an incentive-based scheme that promotes cooperation and enforces fair exchange of resources among peers. These mechanisms provide the basis for the development of distributed self-organizing algorithms to automate PR and, through incentives, maximize their effectiveness in realistic P2P environments. Our proposed solution is evaluated using a combination of analytical and experimental methods. The analytical models are developed to determine the availability and repair cost properties of PR. The results indicate that PR’s repair cost outperforms other redundancy schemes. The experimental analysis was carried out using simulation and the development of a testbed. The simulation results confirm that PR improves content availability in P2P. The proposed mechanisms are implemented and tested using a DHT-based P2P application environment. The experimental results indicate that the incentive-based mechanism can promote fair exchange of resources and limits the impact of uncooperative behaviors such as “free-riding”

O(d,d) invariance at two and three loops

We show that in a two-dimensional sigma-model whose fields only depend on one target space co-ordinate, the O(d,d) invariance of the conformal invariance conditions observed at one loop is preserved at two loops (in the general case with torsion) and at three loops (in the case without torsion).Comment: 21 pages. Plain Tex. Uses Harvmac ("b" option). Revised Version with references added and minor errors correcte