Abstract
The double field theory monopole solution by Berman and Rudolph is shown to reproduce non-geometric backgrounds with non-vanishing Q- and R-flux upon an appropriate choice of physical and dual coordinates. The obtained backgrounds depend non-trivially on dual coordinates and have only trivial monodromies. Upon smearing the solutions along the dual coordinates one reproduces the known $5^2_2$ solution for the Q-brane and co-dimension 1 solution for the R-brane. The T-duality invariant magnetic charge is explicitly calculated for all these backgrounds and is found to be equal to the magnetic charge of (unsmeared) NS5-brane.
Highlights
Solution of the section condition is to drop all dependence on the ‘winding’ coordinates xμ and the theory reproduces conventional supergravity
Components of the generalised metric corresponding to different choices of the physical subspace are related to each other by Buscher rules [10] realising the notion of T-duality transformation in Double Field Theory
This observation was made precise by Tong [38] where he showed that the two-dimensional gauged linear sigma model underlying the smeared NS5-brane receives worldsheet instanton corrections of precisely the type discussed above
Summary
We briefly explain the idea of worldsheet instanton corrections to the background of H- and KK-monopole. This observation was made precise by Tong [38] where he showed that the two-dimensional gauged linear sigma model underlying the smeared NS5-brane (that is T-dual to the Kaluza-Klein monopole) receives worldsheet instanton corrections of precisely the type discussed above.2 In this way, worldsheet instantons are related to localisation in the S1 direction of the transverse space of the NS5-brane. In the T-dual picture of the Kaluza-Klein monopole this localisation effect does not occur in the usual ‘momentum’ space but in the dual ‘winding’ space of the string This point of view was emphasised in [29] and the corresponding double field theory interpretation was given later in [30] where it was shown that the worldsheet instantons in this language naturally provide an origin of dual coordinates after T-duality of a solution that is localised and not smeared. T-duality on the smeared Kaluza-Klein monopole [44, 45], see [46, 47] for further discussions of duality orbits of smeared co-dimension two objects
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