Non-commutative/non-associative IIA (IIB) Q- and R-branes and their intersections

TL;DR

This paper constructs and analyzes non-geometric Q- and R-branes in string theory, exploring their properties using double field theory and their implications for non-commutative and non-associative geometries in compactifications.

Contribution

It introduces explicit constructions of non-geometric Q- and R-branes, demonstrating their local and global consistency, and explores their role in supersymmetric intersecting brane configurations.

Findings

Q-branes are well-behaved solutions in double field theory.

Intersecting Q- and R-branes lead to non-geometric flux backgrounds with non-commutative geometry.

Effective superpotentials from non-geometric fluxes are derived.

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, redefined background fields tilde G and beta 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) x SU(3) group structures. In the near horizon limit the intersecting brane configurations lead to type II backgrounds of the form AdS4 x M6, where the six-dimensional compact space M6 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.