Covariant action for a string in doubled yet gauged spacetime

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 <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold">O</mi><mo stretchy="false">(</mo><mi>D</mi><mo>,</mo><mi>D</mi><mo stretchy="false">)</mo></math> 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