Covariant action for a string in doubled yet gauged spacetime

TL;DR

This paper develops a covariant string action in a doubled, gauged spacetime framework, demonstrating full symmetry invariance and the natural emergence of a topological term, advancing the understanding of T-duality and gauge symmetries in string theory.

Contribution

It introduces a covariant string action in doubled yet gauged spacetime with a generalized metric, incorporating gauge symmetry, diffeomorphisms, Weyl symmetry, and T-duality.

Findings

Constructed a fully covariant string action with generalized metric.

Derived a self-duality condition from equations of motion.

Showed the action couples consistently to T-dual backgrounds with singular metrics.

Abstract

The section condition in double field theory has been shown to imply that a physical point should be one-to-one identified with a gauge orbit in the doubled coordinate space. Here we show the converse is also true, and continue to explore the idea of `spacetime being doubled yet gauged'. Introducing an appropriate gauge connection, we construct a string action, with an arbitrary generalized metric, which is completely covariant with respect to the coordinate gauge symmetry, generalized diffeomorphisms, world-sheet diffeomorphisms, world-sheet Weyl symmetry and O(D,D) T-duality. A topological term previously proposed in the literature naturally arises and a self-duality condition follows from the equations of motion. Further, the action may couple to a T-dual background where the Riemannian metric becomes everywhere singular.