Observations on integral and continuous U-duality orbits in N=8 supergravity
File(s)
Accepted version
Author(s)
Type
Journal Article
Abstract
One would often like to know when two a priori distinct extremal black p-brane solutions are in fact related by U-duality. In the classical supergravity limit the answer for a large class of theories has been known for some time now. However, in the full quantum theory the U-duality group is broken to a discrete subgroup, a consequence of the Dirac–Zwanziger–Schwinger charge quantization conditions. The question of U-duality orbits in this case is a nuanced matter. In the present work we address this issue in the context of \mathcal {N}=8 supergravity in four, five and six dimensions. The purpose of this paper is to present and clarify what is currently known about these orbits while at the same time filling in some of the details not yet appearing in the literature. For the continuous case we present the cascade of relationships existing between the orbits, generated as one descends from six to four dimensions, together with the corresponding implications for the associated moduli spaces. In addressing the discrete case we exploit the mathematical framework of integral Jordan algebras, the integral Freudenthal triple system and, in particular, the work of Krutelevich. The charge vector of the dyonic black string in D = 6 is SO(5,5; \mathds{Z}) related to a two-charge reduced canonical form uniquely specified by a set of two arithmetic U-duality invariants. Similarly, the black hole (string) charge vectors in D = 5 are E_{6(6)}(\mathds{Z}) equivalent to a three-charge canonical form, again uniquely fixed by a set of three arithmetic U-duality invariants. However, the situation in four dimensions is, perhaps predictably, less clear. While black holes preserving more than 1/8 of the supersymmetries may be fully classified by the known arithmetic E_{7(7)}(\mathds{Z}) invariants, 1/8-BPS and non-BPS black holes yield increasingly subtle orbit structures, which remain to be properly understood. However, for the very special subclass of projective black holes a complete classification is known. All projective black holes are E_{7(7)}(\mathds{Z}) related to a four- or five-charge canonical form determined uniquely by the set of known arithmetic U-duality invariants. Moreover, E_{7(7)}(\mathds{Z}) acts transitively on the charge vectors of projective black holes with a given leading-order entropy.
Date Issued
2010-09-21
Date Acceptance
2010-05-13
Citation
Classical and Quantum Gravity, 2010, 27 (18)
ISSN
0264-9381
Publisher
IOP Publishing
Journal / Book Title
Classical and Quantum Gravity
Volume
27
Issue
18
Copyright Statement
© 2010 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article accepted for publication in Classical and Quantum Gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at https://dx.doi.org/10.1088/0264-9381/27/18/185003.
Sponsor
Science and Technology Facilities Council (STFC)
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000280923100004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Grant Number
ST/G000743/1
Subjects
Science & Technology
Physical Sciences
Astronomy & Astrophysics
Quantum Science & Technology
Physics, Multidisciplinary
Physics, Particles & Fields
Physics
MAXWELL-EINSTEIN SUPERGRAVITY
BLACK-HOLE ENTROPY
JORDAN ALGEBRAS
DIVISION-ALGEBRAS
ATTRACTORS
OCTONIONS
SUPERSYMMETRY
ENTANGLEMENT
TRIALITY
SPINORS
Publication Status
Published
Article Number
185003
Date Publish Online
2010-07-27