On the Non-commutativity of Closed String Zero Modes

Abstract

We explore several consequences of the recently discovered intrinsic non-commutativity of the zero-mode sector of closed string theory. In particular, we illuminate the relation between T-duality and this intrinsic non-commutativity and also note that there is a simple closed string product, equivalent to the splitting-joining interaction of the pants diagram, that respects this non-commutativity and is covariant with respect to T-duality. We emphasize the central role played by the symplectic form $\omega$ on the space of zero modes. Furthermore, we begin an exploration of new non-commutative string backgrounds. In particular, we show that a constant non-geometric background field leads to a non-commutative space-time. We also comment on the non-associativity that consequently arises in the presence of non-trivial flux. In this formulation, the $H$-flux as well as the `non-geometric' $Q$-, $R$- and $F$-fluxes are simply the various components of the flux of an almost symplectic form.

18 pages

References in corpus (8)

• Double Field Theory
• Doubled Geometry and T-Folds
• T-duality and closed string non-commutative (doubled) geometry
• Structure Constants and Integrable Bootstrap in Planar N=4 SYM Theory
• Quantum Gravity, Dynamical Phase Space and String Theory
• Worldsheet CFTs for Flat Monodrofolds
• Twisted Poisson Structures and Non-commutative/non-associative Closed String Geometry
• Is String Interaction the Origin of Quantum Mechanics?

Cited by in corpus (1)

• Modified Dark Matter in Galaxies and Galaxy Clusters