Abstract
In this paper we discuss the construction of non-geometric Q- and R-branes as sources of non-geometric Q- and R-fluxes in string compactifications. The non-geometric Q-branes, being obtained via T-duality from the NS 5-brane or respectively from the KK-monopole, are still local solutions of the standard NS action, where however the background fields G and B possess non-geometric global monodromy properties. We show that using double field theory and redefined background fields \( \widetilde{G} \) and β as well as their corresponding effective action, the Q-branes are locally and globally well behaved solutions. Furthermore the R-brane solution can be at least formally constructed using dual coordinates. We derive the associated non-geometric Q- and R-fluxes and discuss that closed strings moving in the space transversal to the world-volumes of the non-geometric branes see a non-commutative or a non-associative geometry.
In the second part of the paper we construct intersecting Q- and R-brane configurations as completely supersymmetric solutions of type IIA/B supergravity with certain SU(3) × SU(3) group structures. In the near horizon limit the intersecting brane configurations lead to type II backgrounds of the form AdS 4 × M 6, where the six-dimensional compact space M 6 is a torus fibration with various non-geometric Q- and R-fluxes in the compact directions. It exhibits an interesting non-commutative and non-associate geometric structure. Furthermore we also determine some of the effective four-dimensional superpotentials originating from the non-geometric fluxes.
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Haßler, F., Lüst, D. Non-commutative/non-associative IIA (IIB) geometries from Q- and R-branes and their intersections. J. High Energ. Phys. 2013, 48 (2013). https://doi.org/10.1007/JHEP07(2013)048
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DOI: https://doi.org/10.1007/JHEP07(2013)048