2012/11/30 by David Andriot, Magdalena Larfors, Dieter Lust +1 · 1 citation
Mathematics · Physics and Astronomy · #hep-th #math-ph #math.MP #math.QA
paper · pdf · doi:10.1007/jhep06(2013)021
47 pages; published version
arxiv created 2013/06/12 · arxiv updated 2015/06/12
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. We use them as well as T-duality to determine, in the non-geometric background, a commutator of two string coordinates, which turns out to be non-vanishing. We relate this non-commutativity to the closed string boundary conditions, and the non-geometric Q-flux.