Hidden Borcherds symmetries in Zn orbifolds of M-theory and magnetized D-branes in type 0’ orientifolds

Abstract

We study T 11−D−q × T q/Zn orbifold compactifications of eleven-dimensional supergravity and M-theory using a purely algebraic method. Given the description of maximal supergravities reduced on square tori as non-linear coset σ-models, we exploit the mapping between scalar fields of the reduced theory and directions in the tangent space over the coset to construct the orbifold action as a non-Cartan preserving finite order inner automorphism of the complexified U-duality algebra. Focusing on the exceptional serie of Cremmer-Julia groups, we compute the residual U-duality symmetry after orbifold projection and determine the reality properties of their corresponding Lie algebras. We carry out this analysis as far as the hyperbolic e10 algebra, conjectured to be a symmetry of M-theory. In this case the residual subalgebras are shown to be described by a special class of Borcherds and Kac-Moody algebras, modded out by their centres and derivations. Furthermore, we construct an alternative description of the orbifold action in terms of equivalence classes of shift vectors, and, in D = 1, we show that a root of e10 can always be chosen as the class representative. Then, in the framework of the E10|10/K(E10|10) effective σ-model approach to M-theory near a spacelike singularity, we identify these roots with brane configurations stabilizing the corresponding orbifolds. In the particular case of Z2 orbifolds of M-theory descending to type 0’ orientifolds, we argue that these roots can be interpreted as pairs of magnetized D9and D9’-branes, carrying the lower-dimensional brane charges required for tadpole cancellation. More generally, we provide a classification of all such roots generating Zn product orbifolds for n 6 6, and hint at their possible interpretation. 1 e-mail address : bagnoud@gauge.scphys.kyoto-u.ac.jp 2 e-mail address : Luca Carlevaro@unine.ch

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Cite this paper

@inproceedings{Carlevaro2006HiddenBS, title={Hidden Borcherds symmetries in Zn orbifolds of M-theory and magnetized D-branes in type 0’ orientifolds}, author={Luca Carlevaro}, year={2006} }