O(D,D) gauge fields in the T-dual string Lagrangian

TL;DR

This paper develops a string Lagrangian framework that makes T-duality manifest by doubling all string modes and treating the gravitational field as an O(D,D) gauge field, ensuring gauge invariance and dual space descriptions.

Contribution

It introduces a Lagrangian formulation with doubled string modes and an O(D,D) gauge field, providing a gauge-invariant approach to manifest T-duality in string theory.

Findings

Lagrangian with doubled string modes and O(D,D) gauge fields

Gauge invariance of the T-duality space line element

Background conditions consistent with O(D,D) symmetry

Abstract

We present the string Lagrangian with manifest T-duality. Not only zero-modes but also all string modes are doubled. The gravitational field is an O(D,D) gauge field. We give a Lagrangian version of the section condition for the gauge invariance which compensates the O(D,D) transformation from the gravitational field and the GL(2D) coordinate transformation. We also show the gauge invariance of the line element of the manifest T-duality space and the O(D,D) condition on the background. Different sections describe dual spaces.