An Introduction to Nonassociative Physics
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.
Cite
@article{arxiv.1903.05673,
title = {An Introduction to Nonassociative Physics},
author = {Richard J. Szabo},
journal= {arXiv preprint arXiv:1903.05673},
year = {2019}
}
Comments
41 pages, 4 figures; v2: minor corrections; Based on Lectures at the Workshop "Dualities and Generalized Geometries", Corfu Summer Institute on Elementary Particle Physics and Gravity, 31 August-28 September 2018, Corfu, Greece; Final version to be published in Proceedings of Science