Covariant action for a string in doubled yet gauged spacetime

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.Comment: 1+29 pages; v2) Refs added. minor changes. To appear in Nuclear Physics

Global aspects of double geometry

“…The local symmetries are the usual ones but described as a particular realisation of a local O(d, d) transformation. This also fits nicely with recent work by Lee and Park on double field theory as a gauged spacetime [39].…”

U-gravity: SL(N)

“…Further, once formulated in terms of genuine O(D, D) covariant variables, DFT does not merely repackage Generalized Geometry or known supergravities, but can also describe non-Riemannian backgrounds where the notion of Riemannian metric ceases to exist even locally [61]. In a somewhat abstract level, the DFT-metric can be defined simply as a 'symmetric O(D, D) element', with which (bosonic) DFT and a doubled string world-sheet action [61] still make sense.…”

“…In a somewhat abstract level, the DFT-metric can be defined simply as a 'symmetric O(D, D) element', with which (bosonic) DFT and a doubled string world-sheet action [61] still make sense. For most ("non-degenerate") cases the DFT-metric can be parametrized by Riemannian metric, g µν and Kalb-Ramond B-field, which allows DFT to describe an ordinary Riemannian gravity.…”

“…An extreme example is the DFT vacuum solution where the DFT-metric coincides with the O(D, D) invariant constant metric. The doubled string action then reduces to a chiral sigma model [61], similar to [62].…”

“…[57,61], imposing the section condition is, in fact, equivalent to postulating an equivalence relation on the doubled coordinate space. That is to say, spacetime is doubled yet gauged.…”