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

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [3]
  1. Pennsylvania State Univ., University Park, PA (United States). Physics Dept. Inst. for Gravitation and the Cosmos
  2. Ludwig Maximilian Univ., Munich (Germany). Dept. of Physics. Arnold Sommerfeld Center for Theoretical Physics; Max Planck Inst. for Physics, Munich (Germany). Werner Heisenberg Inst.
  3. Ludwig Maximilian Univ., Munich (Germany). Dept. of Physics. Arnold Sommerfeld Center for Theoretical Physics
+ Show Author Affiliations

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 gs.

Research Organization:
Pennsylvania State Univ., University Park, PA (United States); Ludwig Maximilian Univ. of Munich, Munich (Germany)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP); European Research Council (ERC)
Contributing Organization:
Max Planck Inst. for Physics, Munich (Germany)
Grant/Contract Number:
SC0010534; 32004
OSTI ID:
1368088
Journal Information:
Journal of High Energy Physics (Online), Vol. 2016, Issue 11; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 23 works
Citation information provided by
Web of Science

References (51)

Magnetic sources and 3-cocycles (comment) journal May 1985
Magnetic charge quantization and angular momentum journal June 1969
Exotic branes in string theory journal November 2013
T-duality without isometry via extended gauge symmetries of 2D sigma models journal January 2016
Geometry and fluxes of SL(5) exceptional field theory journal March 2015
Exceptional supergravity theories and the magic square journal December 1983
Lectures on nongeometric flux compactifications journal October 2007
Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids journal February 2013
Duality, quotients, and currents journal April 1992
Beyond the standard gauging: gauge symmetries of Dirac sigma models journal August 2016
Four-dimensional string compactifications with D-branes, orientifolds and fluxes journal July 2007
T-duality for principal torus bundles journal March 2004
Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT’s journal October 2013
Nongeometric flux compactifications journal October 2005
A ten-dimensional action for non-geometric fluxes journal September 2011
T-duality, generalized geometry and non-geometric backgrounds journal April 2009
(Non-)commutative closed string on T-dual toroidal backgrounds journal June 2013
Double field theory journal September 2009
$T$-duality for torus bundles with $H$-fluxes via noncommutative topology. {II}. The high-dimensional case and the $T$-duality group journal January 2006
T-duality for principal torus bundles and dimensionally reduced Gysin sequences journal January 2005
Conformal and Quasiconformal Realizations¶of Exceptional Lie Groups journal July 2001
Generalized spacetimes defined by cubic forms and the minimal unitary realizations of their quasiconformal groups journal August 2005
Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds journal June 2015
The SO(8) supergravity journal November 1979
A 3-cocycle in quantum mechanics journal February 1985
Non-commutative/non-associative IIA (IIB) geometries from Q- and R-branes and their intersections journal July 2013
Three-Cocycle in Mathematics and Physics journal January 1985
Geometric Action for Nongeometric Fluxes journal June 2012
Exceptional realizations of the lorentz group: Supersymmetries and leptons journal October 1975
The G2 invariant compactifications in eleven-dimensional supergravity journal December 1984
Exotic Branes and Nongeometric Backgrounds journal June 2010
Lectures on Spectrum Generating Symmetries and U-Duality in Supergravity, Extremal Black Holes, Quantum Attractors and Harmonic Superspace book January 2010
The effective action of double field theory journal November 2011
Asymmetric orbifolds, non-geometric fluxes and non-commutativity in closed string theory journal April 2012
T-duality, Quotients and Currents for Non-Geometric Closed Strings: T-duality, Quotients and Currents for Non-Geometric Closed Strings journal August 2015
Generalised T-duality and non-geometric backgrounds journal May 2006
The O D, D geometry of string theory journal May 2014
A geometry for non-geometric string backgrounds journal October 2005
Nonassociative Tori and Applications to T-Duality journal March 2006
The local symmetries of M-theory and their formulation in generalised geometry journal January 2012
T-Duality: Topology Change from H-Flux journal June 2004
The parallelizing S7 torsion in gauged N=8 supergravity journal January 1984
New supersymmetric string compactifications journal March 2003
Non-associative deformations of geometry in double field theory journal April 2014
Quark structure and octonions journal November 1973
Non-geometric fluxes in supergravity and double field theory journal June 2012
Quasiconformal Realizations of $E_{6(6)}, E_{7(7)}, E_{8(8)}$ and $SO(n+3,m+3), N=4 and N>4$ Supergravity and Spherical Vectors journal January 2009
Flux compactifications in string theory: A comprehensive review journal January 2006
$E_8$ gauge theory, and a derivation of $K$-theory from $M$-theory journal January 2002
Nonassociativity, Malcev algebras and string theory journal April 2013
The intriguing structure of non-geometric frames in string theory: Non-geometric frames in string theory journal July 2013

Cited By (9)

Locally non-geometric fluxes and missing momenta in M-theory journal January 2018
Fluxes in exceptional field theory and threebrane sigma-models journal May 2019
Weaving the exotic web journal September 2018
Nearly associative deformation quantization journal April 2018
Recurrence relations for symplectic realization of (quasi)-Poisson structures journal May 2019
Constructions of L ∞ Algebras and Their Field Theory Realizations journal November 2018
Locally non-geometric fluxes and missing momenta in M-theory text January 2017
Nearly associative deformation quantization text January 2018
Fluxes in Exceptional Field Theory and Threebrane Sigma-Models text January 2019

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Flux compactifications
M-Theory
Non-Commutative Geometry
String Duality