Perturbations of Pulsating Strings

We discuss semiclassical quantization of circular pulsating strings in AdS3 x S3 background with and without the Neveu-Schwarz- Neveu-Schwarz (NS-NS) flux. We find the equations of motion corresponding to the quadratic action in bosonic sector in terms of scalar quantities and invariants of the geometry. The general equations for studying physical perturbations along the string in an arbitrary curved spacetime are written down using covariant formalism. We discuss the stability of these string configurations by studying the solutions of the linearized perturbed equations of motion.Comment: 18 pages, to appear in EPJ

Moving constraints as stabilizing controls in classical mechanics

The paper analyzes a Lagrangian system which is controlled by directly assigning some of the coordinates as functions of time, by means of frictionless constraints. In a natural system of coordinates, the equations of motions contain terms which are linear or quadratic w.r.t.time derivatives of the control functions. After reviewing the basic equations, we explain the significance of the quadratic terms, related to geodesics orthogonal to a given foliation. We then study the problem of stabilization of the system to a given point, by means of oscillating controls. This problem is first reduced to the weak stability for a related convex-valued differential inclusion, then studied by Lyapunov functions methods. In the last sections, we illustrate the results by means of various mechanical examples.Comment: 52 pages, 4 figure

Holographic d-wave superconductors

We construct top down models for holographic d-wave superfluids in which the order parameter is a charged spin two field in the bulk. Close to the transition temperature the condensed phase can be captured by a charged spin two field in an R-charged black hole background (downstairs picture) or equivalently by specific graviton perturbations of a spinning black brane (upstairs picture). We analyse the necessary conditions on the mass and the charge of the spin two field for a condensed phase to exist and we discuss the competition of the d-wave phase with other phases such as s-wave superfluids.Comment: 58 pages, 7 figure

Supercriticality of a Class of Critical String Cosmological Solutions

For a class of Friedmann-Robertson-Walker type string solutions with compact hyperbolic spatial slices formulated in critical dimension, we find the world sheet conformal field theory which involves the linear dilaton and Wess-Zumino-Witten type model with the compact hyperbolic target space. By analyzing the infrared spectrum, we conclude that the theory is actually supercritical due to the modular invariance of string theory. Thus, taking into account previous results, we conclude that all the simple nontrivial string cosmological solutions are supercritical. A possible explanation of why we are living in D=4 is provided. The interesting relation of this background with the Supercritical String Cosmology (SSC) is pointed out