Branes and polytopes. (3rd September 2019)

• Record Type: Journal Article
• Authors: Romano, Luca
• Is Part Of: Journal of physics. Volume 52:Number 39(2019)
• Publication Date: 2019-09-03
• Subjects: supergravity -- p-brane -- U-duality -- string theory -- Coxeter group -- Weyl group -- wrapping rules; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ab3a1f
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We investigate the hierarchies of half-supersymmetric branes in maximal supergravity theories. By studying the action of the Weyl group of the U-duality group of maximal supergravities we discover a set of universal algebraic rules describing the number of independent 1/2-BPS p-branes, rank by rank, in any dimension. We show that these relations describe the symmetries of certain families of uniform polytopes. This induces a correspondence between half-supersymmetric branes and vertices of opportune uniform polytopes. We show that half-supersymmetric 0-, 1- and 2-branes are in correspondence with the vertices of the k 21, 2 k 1 and 1 k 2 families of uniform polytopes, respectively, while 3-branes correspond to the vertices of the rectified version of the 2 k 1 family. For 4-branes and higher rank solutions we find a general behavior. The interpretation of half-supersymmetric solutions as vertices of uniform polytopes reveals some intriguing aspects. One of the most relevant is a triality relation between 0-, 1- and 2-branes.