Super-exceptional embedding construction of the M5-brane

An article that we have written:

Abstract. In the further quest to mathematically formulating M-theory, we consider three major open problems: A first-principles construction of the single (abelian) M5-brane Lagrangian density, second the gauge enhancement in heterotic M-theory, and third the superymmetric enhancement of exceptional M-geometry. By combining techniques from homotopy theory and from supergeometry to what we call super homotopy theory, we present an elegant joint solution to all three problems: After explaining how charge-quantization of the C-field in Cohomotopy reveals D'Auria-Fré‘s “hidden supergroup” of 11d supergravity as the super-exceptional target space, in the sense of Bandos, for M5-brane sigma-models, we prove, in exceptional generalization of the “doubly supersymmetric” superembedding formalism, that a Perry-Schwarz-type Lagrangian for single (abelian) 𝒩=(1,0)\mathcal{N} = (1,0) M5-branes emerges as the super-exceptional trivialization of the M5-brane cocycle along the super-exceptional embedding of the "half" M5-brane locus, super-exceptionally compactified on the Hořava-Witten circle fiber.

From inspection of the resulting 5d super Yang-Mills Lagrangian we find that the extra fermion field appearing in super-exceptional M-geometry, whose physical interpretation had remained open, is the M-theoretic avatar of the gaugino field on the heterotic MO9-planes.

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Last revised on August 3, 2019 at 18:03:54. See the history of this page for a list of all contributions to it.