An Introduction to Nonassociative Physics

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Abstract

We give a pedagogical introduction to the nonassociative structures arising from recent developments in quantum mechanics with magnetic monopoles, in string theory and M-theory with non-geometric fluxes, and in M-theory with non-geometric Kaluza-Klein monopoles. After a brief overview of the main historical appearences of nonassociativity in quantum mechanics, string theory and M-theory, we provide a detailed account of the classical and quantum dynamics of electric charges in the backgrounds of various distributions of magnetic charge. We apply Born reciprocity to map this system to the phase space of closed strings propagating in R-flux backgrounds of string theory, and then describe the lift to the phase space of M2-branes in R-flux backgrounds of M-theory. Applying Born reciprocity maps this M-theory configuration to the phase space of M-waves probing a non-geometric Kaluza-Klein monopole background. These four perspective systems are unified by a covariant 3-algebra structure on the M-theory phase space.
Original languageEnglish
Article number100
JournalProceedings of Science
Volume347
DOIs
Publication statusPublished - 19 Sep 2019
EventCorfu Summer Institute 2018 "School and Workshops on Elementary Particle Physics and Gravity" - Corfu, Greece
Duration: 31 Aug 201828 Sep 2018

Keywords

  • hep-th
  • math-ph
  • math.MP
  • math.QA
  • math.SG

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