Quantum Mechanics of the Doubled Torus

Abstract

We investigate the quantum mechanics of the doubled torus system, introduced by Hull [1] to describe T-folds in a more geometric way. Classically, this system consists of a world-sheet Lagrangian together with some constraints, which reduce the number of degrees of freedom to the correct physical number. We consider this system from the point of view of constrained Hamiltonian dynamics. In this case the constraints are second class, and we can quantize on the constrained surface using Dirac brackets. We perform the quantization for a simple T-fold background and compare to results for the conventional non-doubled torus system. Finally, we formulate a consistent supersymmetric version of the doubled torus system, including supersymmetric constraints.

31 pages, 1 figure; v2: references added, minor corrections to final section

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Cited by in corpus (23)

• Double Field Theory
• Generalised Geometry for M-Theory
• Doubled Geometry and T-Folds
• A ten-dimensional action for non-geometric fluxes
• Generalized Flux Vacua
• Background Field Equations for the Duality Symmetric String
• Duality Symmetric Strings, Dilatons and O(d,d) Effective Actions
• The KK-Monopole/NS5-Brane in Doubled Geometry
• Connecting T-duality invariant theories
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• A Double Sigma Model for Double Field Theory
• A worldsheet supersymmetric Newton-Cartan string
• The string partition function in Hull's doubled formalism
• An O(D,D) Invariant Hamiltonian Action for the Superstring
• The Exceptional Sigma Model
• Mirrorfolds with K3 Fibrations
• D-branes in T-fold conformal field theory
• Superstring partition functions in the doubled formalism
• Aspects of the Doubled Worldsheet
• Comparing Double String Theory Actions
• A Note on Supersymmetric Chiral Bosons
• Aspects of M-Theory Brane Interactions and String Theory Symmetries
• Closed String Partition Functions in Toroidal Compactifications of Doubled Geometries