Couplings between a collection of BF models and a set of three-form gauge fields

Consistent interactions that can be added to a free, Abelian gauge theory comprising a collection of BF models and a set of three-form gauge fields are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. Under the hypotheses of smooth, local, PT invariant, Lorentz covariant, and Poincare invariant interactions, supplemented with the requirement on the preservation of the number of derivatives on each field with respect to the free theory, we obtain that the deformation procedure modifies the Lagrangian action, the gauge transformations as well as the accompanying algebra.Comment: 17 page

Superconducting transition in disordered granular superconductors in magnetic fields

Motivated by a recent argument that the superconducting (SC) transition field of three-dimensional (3D) disordered superconductors with granular structure in a nonzero magnetic field should lie above $H_{c2}(0)$ in low $T$ limit, the glass transition (or, in 2D, crossover) curve $H_g(T)$ of disordered quantum Josephson junction arrays is examined by incorporating SC fluctuations. It is found that the glass transition or crossover in the granular materials can be described on the same footing as the vortex-glass (VG) transition in amorphous-like (i.e., nongranular) materials. In most of 3D granular systems, the vanishing of resistivity upon cooling should occur even above $H_{c2}(0)$, while the corresponding sharp drop of the resistivity in 2D case may appear only below $H_{c2}$ as a result of an enhanced quantum fluctuation.Comment: Accepted for publication in Phys. Rev. B. The content of sec.3 in v.2 was removed from here and presented more extensively in a separate paper (cond-mat/0606522) where the argument of nonsuperconducting vortex-glass in cond-mat/0512432 is shown to be fals

AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories

We give a detailed exposition of the Alexandrov-Kontsevich-Schwarz- Zaboronsky superfield formalism using the language of graded manifolds. As a main illustarting example, to every Courant algebroid structure we associate canonically a three-dimensional topological sigma-model. Using the AKSZ formalism, we construct the Batalin-Vilkovisky master action for the model.Comment: 13 pages, based on lectures at Rencontres mathematiques de Glanon 200

Effect of in-plane line defects on field-tuned superconductor-insulator transition behavior in homogeneous thin film

Field-tuned superconductor-insulator transition (FSIT) behavior in 2D isotropic and homogeneous thin films is usually accompanied by a nonvanishing critical resistance at low $T$. It is shown that, in a 2D film including line defects paralle to each other but with random positions perpendicular to them, the (apparent) critical resistance in low $T$ limit vanishes, as in the 1D quantum superconducting (SC) transition, under a current parallel to the line defects. This 1D-like critical resistive behavior is more clearly seen in systems with weaker point disorder and may be useful in clarifying whether the true origin of FSIT behavior in the parent superconductor is the glass fluctuation or the quantum SC fluctuation. As a by-product of the present calculation, it is also pointed out that, in 2D films with line-like defects with a long but {\it finite} correlation length parallel to the lines, a quantum metallic behavior intervening the insulating and SC ones appears in the resistivity curves.Comment: 16 pages, 14 figure

An Alternative Topological Field Theory of Generalized Complex Geometry

We propose a new topological field theory on generalized complex geometry in two dimension using AKSZ formulation. Zucchini's model is $A$ model in the case that the generalized complex structuredepends on only a symplectic structure. Our new model is $B$ model in the case that the generalized complex structure depends on only a complex structure.Comment: 29 pages, typos and references correcte

WZW-Poisson manifolds

We observe that a term of the WZW-type can be added to the Lagrangian of the Poisson Sigma model in such a way that the algebra of the first class constraints remains closed. This leads to a natural generalization of the concept of Poisson geometry. The resulting "WZW-Poisson" manifold M is characterized by a bivector Pi and by a closed three-form H such that [Pi,Pi]_Schouten = .Comment: 4 pages; v2: a reference adde

On the generalized Freedman-Townsend model

Consistent interactions that can be added to a free, Abelian gauge theory comprising a finite collection of BF models and a finite set of two-form gauge fields (with the Lagrangian action written in first-order form as a sum of Abelian Freedman-Townsend models) are constructed from the deformation of the solution to the master equation based on specific cohomological techniques. Under the hypotheses of smoothness in the coupling constant, locality, Lorentz covariance, and Poincare invariance of the interactions, supplemented with the requirement on the preservation of the number of derivatives on each field with respect to the free theory, we obtain that the deformation procedure modifies the Lagrangian action, the gauge transformations as well as the accompanying algebra. The interacting Lagrangian action contains a generalized version of non-Abelian Freedman-Townsend model. The consistency of interactions to all orders in the coupling constant unfolds certain equations, which are shown to have solutions.Comment: LaTeX, 62 page

Geometric Langevin equations on submanifolds and applications to the stochastic melt-spinning process of nonwovens and biology

In this article we develop geometric versions of the classical Langevin equation on regular submanifolds in euclidean space in an easy, natural way and combine them with a bunch of applications. The equations are formulated as Stratonovich stochastic differential equations on manifolds. The first version of the geometric Langevin equation has already been detected before by Leli\`evre, Rousset and Stoltz with a different derivation. We propose an additional extension of the models, the geometric Langevin equations with velocity of constant absolute value. The latters are seemingly new and provide a galaxy of new, beautiful and powerful mathematical models. Up to the authors best knowledge there are not many mathematical papers available dealing with geometric Langevin processes. We connect the first version of the geometric Langevin equation via proving that its generator coincides with the generalized Langevin operator proposed by Soloveitchik, Jorgensen and Kolokoltsov. All our studies are strongly motivated by industrial applications in modeling the fiber lay-down dynamics in the production process of nonwovens. We light up the geometry occuring in these models and show up the connection with the spherical velocity version of the geometric Langevin process. Moreover, as a main point, we construct new smooth industrial relevant three-dimensional fiber lay-down models involving the spherical Langevin process. Finally, relations to a class of self-propelled interacting particle systems with roosting force are presented and further applications of the geometric Langevin equations are given