Locally Anisotropic Gravity and Strings

TL;DR

This paper explores the theory of locally anisotropic spaces, analyzing conditions for string propagation and linking conformal invariance with locally anisotropic gravity field equations.

Contribution

It introduces the framework of locally anisotropic spaces with connections and metrics, and studies string propagation and conformal invariance in these backgrounds.

Findings

Conditions for consistent string propagation in anisotropic spaces

Relationship between conformal invariance and gravity field equations

Analysis of renormalization group beta-function in this context

Abstract

An introduction into the theory of locally anisotropic spaces (modelled as vector bundles provided with compatible nonlinear and distinguished linear connections and metric structures and containing as particular cases different types of Kaluza--Klein and/or extensions of Lagrange and Finsler spaces) is presented. The conditions for consistent propagation of closed strings in locally anisotropic background spaces are analyzed. The connection between the conformal invariance, the vanishing of the renormalization group beta--function of the generalized sigma--model and field equations of locally anisotropic gravity is studied in detail.