(Non-)commutative closed string on T-dual toroidal backgrounds
Abstract
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.
Cite
@article{arxiv.1211.6437,
title = {(Non-)commutative closed string on T-dual toroidal backgrounds},
author = {David Andriot and Magdalena Larfors and Dieter Lust and Peter Patalong},
journal= {arXiv preprint arXiv:1211.6437},
year = {2015}
}
Comments
47 pages; published version