Stringy differential geometry, beyond Riemann

TL;DR

This paper introduces a new differential geometry framework that unifies the metric, two-form gauge field, and dilaton from string theory, making T-duality and gauge symmetries manifest, and reformulating the effective action in a single geometric term.

Contribution

It proposes a novel geometric structure that treats key string theory fields uniformly, incorporates T-duality explicitly, and develops a vielbein formalism with an extended internal symmetry.

Findings

Unified geometric description of metric, B-field, and dilaton.

Reformulation of low energy effective action as a single geometric term.

Development of a vielbein formalism with extended Lorentz symmetry.

Abstract

While the fundamental object in Riemannian geometry is a metric, closed string theories call for us to put a two-form gauge field and a scalar dilaton on an equal footing with the metric. Here we propose a novel differential geometry which treats the three objects in a unified manner, manifests not only diffeomorphism and one-form gauge symmetry but also O(D,D) T-duality, and enables us to rewrite the known low energy effective action of them as a single term. Further, we develop a corresponding vielbein formalism and gauge the internal symmetry which is given by a direct product of two local Lorentz groups, SO(1,D-1) times SO(1,D-1). We comment that the notion of cosmological constant naturally changes.