(Non-)commutative closed string on T-dual toroidal backgrounds

Understand

In this paper we investigate the connection between (non-)geometry and (non-)commutativity of the closed string.

• To this end, we solve the classical string on three T-dual toroidal backgrounds: a torus with H-flux, a twisted torus and a non-geometric background with Q-flux.
• In all three situations we work under the assumption of a dilute flux and consider quantities to linear order in the flux density.
• Furthermore, we perform the first steps of a canonical quantization for the twisted torus, to derive commutators of the string expansion modes.