相关论文: Stringy Jacobi fields in Morse theory

We revisit the existence, background independence and uniqueness of closed, open and open-closed bosonic- and topological string field theory, using the machinery of homotopy algebra. In a theory of classical open- and closed strings, the…

The formulation of covariant brackets on the space of solutions to a variational problem is analyzed in the framework of contact geometry. It is argued that the Poisson algebra on the space of functionals on fields should be read as a…

We define Jacobi forms of indefinite lattice index, and show that they are isomorphic to vector-valued modular forms also in this setting. We also consider several operations of the two types of objects, and obtain an interesting bilinear…

Quadratic Lagrangians are introduced adding surface terms to a free particle Lagrangian. Geodesic equations are used in the context of the Hamilton-Jacobi formulation of constrained sysytem. Manifold structure induced by the quadratic…

It is shown that any second order dynamic equation on a configuration bundle $Q\to R$ of non-relativistic mechanics is equivalent to a geodesic equation with respect to a (non-linear) connection on the tangent bundle $TQ\to Q$. The case of…

The exact effective field equations of motion, corresponding to the perturbative mixed theory of open and closed (2,2) world-sheet supersymmetric strings, are investigated. It is shown that they are only integrable in the case of an abelian…

The complete quantum theory of covariant closed strings is constructed in detail. The action is defined by elementary vertices satisfying recursion relations that give rise to Jacobi-like identities for an infinite chain of string field…

Classical bosonic open string models in fourdimensional Minkowski spacetime are discussed. A special attention is paid to the choice of edge conditions, which can follow consistently from the action principle. We consider lagrangians that…

We study Jacobi matrices on trees whose coefficients are generated by multiple orthogonal polynomials. Hilbert space decomposition into an orthogonal sum of cyclic subspaces is obtained. For each subspace, we find generators and the…

We suggest that the extrinsic curvature and torsion of a bosonic string can be employed as variables in a two dimensional Landau-Ginzburg gauge field theory. Their interpretation in terms of the abelian Higgs multiplet leads to two…

Jacobi sigma models are two-dimensional topological non-linear field theories which are associated with Jacobi structures. The latter can be considered as a generalization of Poisson structures. After reviewing the main properties and…

The supporting worldsheet of a string, membrane, or other higher dimensional brane, is analysed in terms of its first, second, and third fundamental tensors, and its inner and outer curvature tensors. The dynamical equations governing the…

The equation of motion of an extended object in spacetime reduces to an ordinary differential equation in the presence of symmetry. By properly defining of the symmetry with notion of cohomogeneity, we discuss the method for classifying all…

We consider type IIA/B strings in two-dimensions and their projection with respect to the nilpotent space-time supercharge. Based on the ground ring structure, we propose a duality between perturbed type II strings and the topological…

We give in this paper bounds for the Morse indices of a large class of simple geodesics on a surface with a generic metric. To our knowledge these bounds are the first that use only the generic hypothesis on the metric.

We show that Jacobi fields along harmonic maps between suitable spaces preserve conformality, holomorphicity, real isotropy and complex isotropy to first order; this last being one of the key tools in the proof by Lemaire and the author of…

We consider conserved currents in an interacting network of one-dimensional objects (or strings). Singular currents localized on a single string are considered in general, and a formal procedure for coarse-graining over many strings is…

We introduce the notion of spectral flow along a periodic semi-Riemannian geodesic, as a suitable substitute of the Morse index in the Riemannian case. We study the growth of the spectral flow along a closed geodesic under iteration,…

We study the perturbative dynamics of an infinite gravitating Nambu-Goto string within the general-relativistic perturbation framework. We develop the gauge invariant metric perturbation on a spacetime containing a self-gravitating straight…

We develop a spectral analysis of a class of block Jacobi operators based on the conjugate operator method of Mourre. We give several applications including scalar Jacobi operators with periodic coefficients, a class of difference operators…