M5 algebra and SO(5,5) duality

• Published in: The journal of high energy physics Vol. 2013; no. 6; pp. 1 - 19
• Main Authors: Hatsuda, Machiko, Kamimura, Kiyoshi
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.06.2013; Springer Nature B.V
• Subjects: Algebra; Brackets; Classical and Quantum Gravitation; Elementary Particles; Gages; Gauges; High energy physics; M theory; Mathematical analysis; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; String Theory; Transformations (mathematics); Vectors (mathematics); p-branes; Space-Time Symmetries; String Duality; M-Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP06(2013)095

A bstract We present “M5 algebra” to derive Courant brackets of the generalized geometry of T ⊕ Λ 2 T ∗ ⊕ Λ 5 T ∗ : the Courant bracket generates the generalized diffeomorphism including gauge transformations of three and six form gauge fields. The Dirac bracket between selfdual gauge fields on a M5-brane gives a C [3] -twisted contribution to the Courant brackets. For M-theory compactified on a five dimensional torus the U-duality symmetry is SO(5,5) and the M5 algebra basis is in the 16-dimensional spinor representation. The M5 worldvolume diffeomorphism constraints can be written as bilinear forms of the basis and transform as a SO(5,5) vector. We also present an extended space spanned by the 16-dimensional coordinates with section conditions determined from the M5 worldvolume diffeomorphism constraints.