Covariant perturbations in the gonihedric string model

Abstract

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 quadratic mean extrinsic curvature of the worldsheet swept out by the string, and is reparametrization invariant. A general expression for the worldsheet perturbations, guided by Jacobi equations without any early gauge fixing, is obtained. This is manifested through a set of highly coupled nonlinear differential partial equations where the perturbations are described by scalar fields, Φ i , living in the worldsheet. This model contains, as a special limit, to the linear model in the mean extrinsic curvature. In such a case the Jacobi equations specialize to a single wave-like equation for Φ.

Singularities of Osculating Developable Surfaces of Timelike Surfaces along Curves

“…For instance, Rojas introduced a covariant framework to research the stability of small perturbations on the gonihedric string model by variational techniques. A general expression of the world sheet perturbations is displayed in [8]. Singularity theory, on the other hand, which is a direct descendant of differential calculus, appeals to the research about geometry, equations and other disciplines (see ).…”

Perturbations of giant magnons and single spikes in $\mathbb R \times S^2$

“…On one hand, it helps in studying the stability properties of the string dynamics of the closed strings, and finding the quantum string corrections to the Wilson loop expectation value for the open string solutions and on the other hand, it helps us in determining the physical properties of topological defects. Apart from [35,36], related recent works on such perturbations can be found in [42][43][44][45].…”