Natural curvature for manifest T-duality

Abstract

We reformulate the manifestly T-dual description of the massless sector of the closed bosonic string, directly from the geometry associated with the (left and right) affine Lie algebra of the coset space Poincare/Lorentz. This construction initially doubles not only the (spacetime) coordinates for translations but also those for Lorentz transformations (and their dual). As a result, the Lorentz connection couples directly to the string (as does the vielbein), rather than being introduced ad hoc to the covariant derivative as previously. This not only reproduces the old definition of T-dual torsion, but automatically gives a general, covariant definition of T-dual curvature (but still with some undetermined connections).

Minor changes in notations (see e.g. eq.(7), eq.(8)). Some typos corrected: e.g factor "i" in equations (11) and (12). New references added

References in corpus (2)

• Doubled α'-Geometry
• New superspaces/algebras for superparticles/strings

Cited by in corpus (18)

• Double Field Theory at Order ${\alpha }^{\prime }$
• Heterotic $\alpha$'-corrections in Double Field Theory
• Superspace with manifest T-duality from type II superstring
• Ramond-Ramond gauge fields in superspace with manifest T-duality
• T-duality off shell in 3D Type II superspace
• Type II chiral affine Lie algebras and string actions in doubled space
• Consistent Truncations and Dualities
• Generalized Dualities and Supergroups
• Exploring the geometry of supersymmetric double field theory
• Gauging Unbroken Symmetries in F-theory
• Gauged Double Field Theory, Current Algebras and Heterotic Sigma Models
• Pre-potential in the $Ad{S}_5\times S^5$ Type IIB superspace
• F-theory superspace backgrounds
• Type II Double Field Theory in Superspace
• Perturbative F-theory 10-brane and M-theory 5-brane
• O(D,D) gauge fields in the T-dual string Lagrangian
• Manifestly T-dual formulation of AdS space
• M Theory from F Theory