Closed String Partition Functions in Toroidal Compactifications of Doubled Geometries

Understand

We revisit partition functions of closed strings on toroidal backgrounds, including their $\mathbb{Z}_N$ shift orbifolds in the formalism where the dimension of the target space is doubled to make T-duality manifest.

• In such a T-duality covariant formalism, the constraint equation imposes a form of chiral factorization.
• Our computation furnishes a non-trivial consistency check for the quantum worldsheet theory of the doubled sigma model, when strings are placed on general toroidal backgrounds.
• The topological term that mixes the physical space and its T-dual is crucial in demonstrating that chiral factorization works, and that we obtain the correct partition function after imposing the constraints.