Eur. Phys. J. C (2007) 50: 683-689
https://doi.org/10.1140/epjc/s10052-007-0224-8

Regular Article - Theoretical Physics

The geometrical form for the string space-time action

Institute of Physics, 11001, Belgrade, P.O. Box 57, Serbia

^* e-mail: sazdovic@phy.bg.ac.yu

Received: 26 July 2006
Revised: 9 October 2006
Published online: 16 February 2007

Abstract

In the present article, we derive the space-time action of the bosonic string in terms of geometrical quantities. First, we study the space-time geometry felt by a probe bosonic string moving in antisymmetric and dilaton background fields. We show that the presence of the antisymmetric field leads to space-time torsion, and the presence of the dilaton field leads to space-time non-metricity. Using these results we obtain the integration measure for space-time with stringy non-metricity, requiring its preservation under parallel transport. We derive the Lagrangian depending on stringy curvature, torsion and non-metricity.