The geometrical form for the string space-time action

TL;DR

This paper derives a geometrical formulation of the bosonic string's space-time action, incorporating torsion and nonmetricity induced by background fields, and establishes the measure for stringy nonmetricity.

Contribution

It introduces a geometrical framework for the string space-time action that includes torsion and nonmetricity, extending traditional geometric descriptions in string theory.

Findings

Space-time torsion arises from antisymmetric background fields.

Dilaton fields induce space-time nonmetricity.

A new measure for space-time with stringy nonmetricity is derived.

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 probe bosonic string moving in antisymmetric and dilaton background fields. We show that the presence of the antisymmetric field leads to the space-time torsion, and the presence of the dilaton field leads to the space-time nonmetricity. Using these results we obtain the integration measure for space-time with stringy nonmetricity, requiring its preservation under parallel transport. We derive the Lagrangian depending on stringy curvature, torsion and nonmetricity.