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Super-exceptional geometry: origin of heterotic M-theory and super-exceptional embedding construction of M5 | | Domenico Fiorenza
; Hisham Sati
; Urs Schreiber
; | | Date: |
31 Jul 2019 | | Abstract: | In the quest for the mathematical formulation of M-theory, we consider three
major open problems: a first-principles construction of the single (abelian)
M5-brane Lagrangian density, the origin of the gauge field in heterotic
M-theory, and the supersymmetric enhancement of exceptional M-geometry. By
combining techniques from homotopy theory and from supergeometry to what we
call super-exceptional geometry within super-homotopy theory, we present an
elegant joint solution to all three problems. This leads to a unified
description of the Nambu-Goto, Perry-Schwarz, and topological Yang-Mills
Lagrangians in the topologically nontrivial setting. After explaining how
charge quantization of the C-field in Cohomotopy reveals D’Auria-Fre’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 super-embedding formalism, that a
Perry-Schwarz-type Lagrangian for single (abelian) 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 Horava-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. | | Source: | arXiv, 1908.0042 | | Services: | Forum | Review | PDF | Favorites | |
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