Related papers: Stringy Jacobi fields in Morse theory

A relativistic string is usually represented by the Nambu-Goto action in terms of the extremal area of a 2-dimensional timelike submanifold of Minkowski space. Alternatively, a family of classical solutions of the string equation of motion…

We show that an invariant surface allows to construct the Jacobi vector field along a geodesic and construct the formula for the normal component of the Jacobi field. If a geodesic is the transversal intersection of two invariant surfaces…

In this paper it is shown that the space of tight geodesic segments connecting any two vertices in a complex of cycles has finite, uniformly bounded dimension. The dimension is defined in terms of a discrete analogue of Jacobi fields, which…

In this paper we study the dynamics of a statistical ensemble of strings, building on a recently proposed gauge theory of the string geodesic field. We show that this stochastic approach is equivalent to the Carath\'eodory formulation of…

We study the geodesic motion of test particles in the space-time of two Abelian-Higgs strings interacting via their magnetic fields. These bound states of cosmic strings constitute a field theoretical realization of p-q-strings which are…

In the stringy cosmology, we investigate singularities in geodesic surface congruences for the time-like and null strings to yield the Raychaudhuri type equations possessing correction terms associated with the novel features owing to the…

We study the semiclassical partition function in the frame work of the Morse theory, to clarify the phase factor of the partition function and to relate it to the eta invariant of Atiyah. Converting physical system with potential into a…

We study geodesic motion in expanding spherical impulsive gravitational waves propagating in a Minkowski background. Employing the continuous form of the metric we find and examine a large family of geometrically preferred geodesics. For…

Perturbations of a class of semiclassical strings known today as spiky strings, are studied using the well-known Jacobi equations for small normal deformations of an embedded timelike surface. It is shown that there exists finite normal…

We briefly review the equations of motion and the space-time interval due to the nonlinear cosmic string that have been derived in ref. [3] for the first time. The different types of isotropic and nonisotropic geodesic lines in the…

We provide a covariant framework to study classically the stability of small perturbations on the so-called gonihedric string model by making precise use of variational techniques. The local action depends of the square root of the…

We find a class of solutions of Einstein's field equations representing spacetime outside a spinning cosmic string surrounded by a gas of non-spinning cosmic strings, and show that there exist closed timelike geodesics in this spacetime.

Geodesics in moduli spaces of string vacua are important objects in string phenomenology. In this paper, we highlight a simple condition that connects brane tensions, including particle masses, with geodesics in moduli spaces. Namely, when…

We give evidence that the all genus amplitudes of topological string theory on compact elliptically fibered Calabi-Yau manifolds can be written in terms of meromorphic Jacobi forms whose weight grows linearly and whose index grows…

In this paper, we establish a "global" Morse index theorem. Given a hypersurface $M^{n}$ of constant mean curvature, immersed in $\mathbb{R}^{n+1}$. Consider a continuous deformation of "generalized" Lipschitz domain $D(t)$ enlarging in…

We study the self-similar motion of a string in a self-similar spacetime by introducing the concept of a self-similar string, which is defined as the world sheet to which a homothetic vector field is tangent. It is shown that in Nambu-Goto…

This review summarizes the recent developments in topological string theory from the author's perspective, mostly focused on aspects of research in which the author is involved. After a brief overview of the theory, we discuss two aspects…

Within the framework of generalized Papapetrou method, we derive the effective equations of motion for a string with two particles attached to its ends, along with appropriate boundary conditions. The equations of motion are the usual…

We analyze the consequences of a recent argument justifying the validity of the "geodesic rule" which can be used to determine the density of global topological defects. We derive a formula that provides a rough estimate of the number of…

We associate a Jacobi form over a rank s lattice to N=2, D=4 heterotic string compactifications which have s Wilson lines at a generic point in the vector multiplet moduli space. Jacobi forms of index m=1 and m=2 have appeared earlier in…