M5 algebra and SO(5,5) duality

Understand

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