M5 algebra and SO(5,5) duality

Abstract

We present "M5 algebra" to derive Courant brackets of the generalized geometry of $T\oplus {\Lambda }^2{T}^{\ast }\oplus {\Lambda }^5{T}^{\ast }$: 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.

18 pages, v2: Eqs. (3.7) and (3.10), comments and references added. v3: minor corrections, to appear in JHEP

References in corpus (16)

• Double Field Theory
• Generalised Geometry for M-Theory
• The gauge algebra of double field theory and Courant brackets
• Generalized Geometry and M theory
• Gauged Double Field Theory
• Extended geometry and gauged maximal supergravity
• Lectures on Generalized Complex Geometry for Physicists
• Stringy Unification of Type IIA and IIB Supergravities under N=2 D=10 Supersymmetric Double Field Theory
• Ramond-Ramond Cohomology and O(D,D) T-duality
• Deformations of calibrated D-branes in flux generalized complex manifolds
• U-geometry : SL(5)
• D-branes and doubled geometry
• D-branes in Generalized Geometry and Dirac-Born-Infeld Action
• E8 duality and dual gravity
• Exceptional geometry and tensor fields
• D-brane couplings and Generalised Geometry

Cited by in corpus (17)

• The Geometry, Branes and Applications of Exceptional Field Theory
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Superspace with manifest T-duality from type II superstring
• Non-linear Kaluza-Klein theory for dual fields
• Ramond-Ramond gauge fields in superspace with manifest T-duality
• Non-Abelian U-duality for membrane
• The Exceptional Sigma Model
• Branes in Extended Spacetime: Brane Worldvolume Theory Based on Duality Symmetry
• Membrane Duality Revisited
• Effective Action for Non-Geometric Fluxes from Duality Covariant Actions
• Exceptional M-brane sigma models and $\eta$-symbols
• Currents, charges and algebras in exceptional generalised geometry
• Gauging Unbroken Symmetries in F-theory
• Gauge Transformation of Double Field Theory for Open String
• Perturbative F-theory 10-brane and M-theory 5-brane
• Five-brane Current Algebras in Type II String Theories
• M Theory from F Theory