Abstract
We construct a world-sheet action for Green-Schwarz superstring in terms of doubled-yet-gauged spacetime coordinates. For an arbitrarily curved NS-NS background, the action possesses $\mathbf{O}(10,10)$ T-duality, $\mathbf{Spin}(1,9)\times\mathbf{Spin}(9,1)$ Lorentz symmetry, coordinate gauge symmetry, spacetime doubled-yet-gauged diffeomorphisms, world-sheet diffeomorphisms and Weyl symmetry. Further, restricted to flat backgrounds, it enjoys maximal spacetime supersymmetry and kappa-symmetry. After the auxiliary coordinate gauge symmetry potential being integrated out, our action can consistently reduce to the original undoubled Green-Schwarz action. Thanks to the twofold spin groups, the action is unique: it is specific choices of the NS-NS backgrounds that distinguish IIA or IIB, as well as lead to non-Riemannian or non-relativistic superstring a la Gomis-Ooguri which might deserve the nomenclature, type IIC.
Highlights
On the doubled coordinate space, T-duality becomes a run-of-the-mill O(D, D) rotation.1 despite of the doubling, the physical dimension of the spacetime should be undoubled: the doubled coordinates must describe D-dimensional physics
After the auxiliary coordinate gauge symmetry potential being integrated out, our action can consistently reduce to the original undoubled Green-Schwarz action
One governing geometric principle, proposed in [13] and pursued in this work, is the notion of doubledyet-gauged coordinate system: the doubled coordinate space is gauged by an equivalence relation, called coordinate gauge symmetry, xM ∼ xM + J MN Φs∂N Φt, (1.2)
Summary
Firstly we present our main result, i.e. ‘the construction of the GreenSchwarz superstring action on the doubled-yet-gauged spacetime’, and provide the relevant explanations, such as the conventions, the field contents, the target-spacetime supersymmetry and the kappa-symmetry. ‘the construction of the GreenSchwarz superstring action on the doubled-yet-gauged spacetime’, and provide the relevant explanations, such as the conventions, the field contents, the target-spacetime supersymmetry and the kappa-symmetry. 2.1 Main result We propose the Green-Schwarz superstring action on the doubled-yet-gauged spacetime,. Equipped with the map from the string world-sheet to the doubled-yet-gauged targetspacetime, σi −→ XM = Xμ , Xν ,. For an arbitrarily curved NS-NS background, the action possesses the manifest O(10, 10) T-duality, the Spin(1, 9) × Spin(9, 1) global Lorentz symmetry, the coordinate gauge symmetry, the target-spacetime doubled-yet-gauged diffeomorphisms over any Killing direction, world-sheet diffeomorphisms and Weyl symmetry. It is worth while to note that, using the properties of the coordinate gauge symmetry potential (1.11), we may rewrite the world-sheet topological term as ǫij DiXM (AjM − iΣjM ) = ǫij ΠM i AjM − i∂iXM ΣjM
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