Triproducts, nonassociative star products and geometry of R-flux string compactifications

Paolo Aschieri, Richard J. Szabo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

18 Citations (Scopus)

Abstract

We elucidate relations between different approaches to describing the nonassociative deformations of geometry that arise in non-geometric string theory. We demonstrate how to derive configuration space triproducts exactly from nonassociative phase space star products and extend the relationship in various directions. By foliating phase space with leaves of constant momentum we obtain families of Moyal-Weyl type deformations of triproducts, and we generalize them to new triproducts of differential forms and of tensor fields. We prove that nonassociativity disappears on-shell in all instances. We also extend our considerations to the differential geometry of nonassociative phase space, and study the induced deformations of configuration space diffeomorphisms. We further develop general prescriptions for deforming configuration space geometry from the nonassociative geometry of phase space, thus paving the way to a nonassociative theory of gravity in non-geometric flux compactifications of string theory.

Original languageEnglish
Title of host publicationConceptual and Technical Challenges for Quantum Gravity 2014 – Parallel session: Noncommutative Geometry and Quantum Gravity
EditorsP Martinetti, J-C Wallet, G Amelino-Camelia
PublisherIOP Publishing
Number of pages32
DOIs
Publication statusPublished - 2015
EventConceptual and Technical Challenges for Quantum Gravity 2014 - Rome, Italy
Duration: 8 Sep 201412 Sep 2014

Publication series

NameJournal of Physics Conference Series
PublisherIOP Publishing
Volume634
ISSN (Print)1742-6588

Conference

ConferenceConceptual and Technical Challenges for Quantum Gravity 2014
CountryItaly
CityRome
Period8/09/1412/09/14

Keywords

  • FIELD-THEORY
  • NONCOMMUTATIVE GEOMETRY
  • D-BRANE
  • SPACETIME

Cite this

Aschieri, P., & Szabo, R. J. (2015). Triproducts, nonassociative star products and geometry of R-flux string compactifications. In P. Martinetti, J-C. Wallet, & G. Amelino-Camelia (Eds.), Conceptual and Technical Challenges for Quantum Gravity 2014 – Parallel session: Noncommutative Geometry and Quantum Gravity (Journal of Physics Conference Series; Vol. 634). IOP Publishing . https://doi.org/10.1088/1742-6596/634/1/012004