M5 algebra and SO(5,5) duality

TL;DR

This paper introduces the M5 algebra to derive generalized geometry structures, revealing how Courant brackets incorporate gauge transformations and exhibit SO(5,5) duality symmetry in M-theory compactifications.

Contribution

It develops the M5 algebra framework to derive Courant brackets and explores the SO(5,5) duality symmetry in M-theory on a five-torus, including the extended space formulation.

Findings

Courant brackets include gauge transformations of three and six form fields.

M5 algebra basis transforms as SO(5,5) spinor representation.

Extended space with 16-dimensional coordinates is consistent with constraints.

Abstract

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. We also present an extended space spanned by the 16-dimensional coordinates with section conditions determined from the M5 worldvolume diffeomorphism constraints.