A geometrical action for dilaton gravity

TL;DR

This paper introduces a geometrical action principle for dilaton gravity involving non-Riemannian, metric-compatible connections with a non-parallel volume element, derived from string theory low-energy limits.

Contribution

It presents a novel geometrical action for dilaton gravity based on a non-Riemannian, metric-compatible connection with a non-parallel volume element, contrasting with previous models.

Findings

Derived from string theory low-energy limits.

Proposed a geometrical action principle for dilaton gravity.

Contrasted with existing axi-dilaton gravity models.

Abstract

We study the gravitational interaction involving the dilaton and the anti-symmetrical $B_{\mu\nu}$ fields that arises in the low-energy limit of string theory. It is shown that such interaction can be derived from a geometrical action principle, with the scalar of curvature of a non-Riemannian, but {\em metric-compatible}, connection as the lagrangian, and with a non-parallel volume-element. This action is contrasted with the recently proposed geometrical action for the 4-dimensional axi-dilaton gravity.