String Theory In Curved Space-Time

TL;DR

This paper investigates the geometric properties of strings in curved space-time, deriving equations of motion, energy-momentum tensor, and analyzing quantum divergences, highlighting asymptotic freedom in extrinsic curvature interactions.

Contribution

It introduces a formulation focusing on string immersion coordinates and explores quantum properties like 1-loop divergences and asymptotic freedom.

Findings

Derived classical equations of motion and energy-momentum tensor.

Calculated 1-loop divergent terms using background field method.

Established asymptotic freedom of extrinsic curvature coupling.

Abstract

Intrinsic and extrinsic geometric properties of string world sheets in curved space-time background are explored. In our formulation, the only dynamical degrees of freedom of the string are its immersion coordinates. Classical equation of motion and the space-time energy-momentum tensor of the string are obtained. The equations of motion for the extrinsic curvature action are second order for the scalar mean curvature of the world sheet. 1-loop divergent terms are calculated using the background field method. Asymptotic freedom of the extrinsic curvature coupling is established.