Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds

We use a T-duality invariant action to investigate the behaviour of a string in non-geometric backgrounds, where there is a non-trivial global $O(D,D)$ patching or monodromy. This action leads to a set of Dirac brackets describing the dynamics of the doubled string, with these brackets determined only by the monodromy. This allows for a simple derivation of non-commutativity and non-associativity in backgrounds which are (even locally) non-geometric. We focus here on the example of the three-torus with H-flux, finding non-commutativity but not non-associativity, and also comment on the relation to the exotic $5^2_2$ brane, which shares the same monodromy.Comment: 31 pages, v2: refs added, corrections to sec 5, results updated, v3: published version with additional discussion in sec

Conserved Currents of Double Field Theory

We find the conserved current associated to invariance under generalised diffeomorphisms in double field theory. This can be used to define a generalised Komar integral. We comment on its applications to solutions, in particular to the fundamental string/pp-wave. We also discuss the current in the context of Scherk-Schwarz compactifications. We calculate the current for both the original double field theory action, corresponding to the NSNS sector alone, and for the RR sector.Comment: 30 pages + appendix, v2: belated update to match published version (typos + refs fixed, some minor comments added