Quantum Mechanics of the Doubled Torus

TL;DR

This paper explores the quantum mechanics of the doubled torus system, a geometric approach to T-folds, by analyzing its constrained Hamiltonian dynamics, performing quantization, and extending it to a supersymmetric version.

Contribution

It provides the first quantization of the doubled torus system with second class constraints and introduces a supersymmetric extension.

Findings

Quantized the doubled torus system using Dirac brackets.

Compared doubled and conventional torus systems.

Formulated a supersymmetric version with consistent constraints.

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.