Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes

Abstract

We propose a non-associative phase space algebra for M-theory backgrounds with locally non-geometric fluxes based on the non-associative algebra of octonions. Our proposal is based on the observation that the non-associative algebra of the non-geometric R-flux background in string theory can be obtained by a proper contraction of the simple Malcev algebra generated by imaginary octonions. Furthermore, by studying a toy model of a four-dimensional locally non-geometric M-theory background which is dual to a twisted torus, we show that the non-geometric background is "missing" a momentum mode. The resulting seven-dimensional phase space can thus be naturally identified with the imaginary octonions. This allows us to interpret the full uncontracted algebra of imaginary octonions as the uplift of the string theory R-flux algebra to M-theory, with the contraction parameter playing the role of the string coupling constant $g_s$.

27 pages

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• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Double Field Theory
• T-duality and closed string non-commutative (doubled) geometry
• Lectures on Nongeometric Flux Compactifications
• T-duality for principal torus bundles
• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• Non-geometric branes are DFT monopoles
• Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds
• Twisted Poisson Structures and Non-commutative/non-associative Closed String Geometry
• Beyond the standard gauging: gauge symmetries of Dirac Sigma Models

Cited by in corpus (8)

• $G_2$-structures and quantization of non-geometric M-theory backgrounds
• Locally non-geometric fluxes and missing momenta in M-theory
• $L_{\infty }$-Bootstrap Approach to Non-Commutative Gauge Theories
• Fluxes in Exceptional Field Theory and Threebrane Sigma-Models
• Nonassociative geometric and quantum information flows and R-flux deformations of wormhole solutions in string gravity
• Nonassociative black holes in R-flux deformed phase spaces and relativistic models of G. Perelman thermodynamics
• Decoupling and integrability of nonassociative vacuum phase space gravitational equations with star and R-flux parametric deformations
• Nonassociative Ricci flows, star product and R-flux deformed black holes, and swampland conjectures