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P. Bouwknegt, K. C. Hannabuss and V. Mathai, “Nonassociative tori and applications to T-duality,” Commun. Math. Phys. 264
2006
Earlier work this paper cites.
E. Beggs and S. Majid, “Nonassociative Riemannian geometry by twisting,” J. Phys. Conf. Ser. 254
Original
2010
Earlier work this paper cites.
D. Lüst, “T-duality and closed string noncommutative (doubled) geometry,” JHEP 1012
Original
2010
Earlier work this paper cites.
R. Blumenhagen and E. Plauschinn, “Nonassociative gravity in string theory?,” J. Phys. A 44
Original
2011
Earlier work this paper cites.
R. Blumenhagen, A. Deser, D. Lüst, E. Plauschinn and F. Rennecke, “Non-geometric fluxes, asymmetric strings and nonassociative geometry,” J. Phys. A 44
Original
2011
Earlier work this paper cites.
P. Bouwknegt, K. C. Hannabuss and V. Mathai, “ C ∗ C^{*} -algebras in tensor categories,” Clay Math. Proc. 12
2011
Earlier work this paper cites.
D. Lüst, “Twisted Poisson structures and noncommutative/nonassociative closed string geometry,” PoS CORFU 2011
Original
2011
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E. Plauschinn, “Non-geometric fluxes and nonassociative geometry,” PoS CORFU 2011
Original
2011
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C. Condeescu, I. Florakis and D. Lüst, “Asymmetric orbifolds, non-geometric fluxes and noncommutativity in closed string theory,” JHEP 1204
Original
2012
Earlier work this paper cites.

Similar

K. C. Hannabuss and V. Mathai, “Nonassociative strict deformation quantization of C ∗ C^{*} -algebras and nonassociative torus bundles,” Lett. Math. Phys. 102
Original
2012
Cited alongside, same era.
D. Mylonas, P. Schupp and R. J. Szabo, “Membrane sigma-models and quantization of non-geometric flux backgrounds,” JHEP 1209
Original
2012
Cited alongside, same era.
D. Andriot, M. Larfors, D. Lüst and P. Patalong, “(Non)commutative closed string on T-dual toroidal backgrounds,” JHEP 1306
Original
2013
Cited alongside, same era.
A. Chatzistavrakidis and L. Jonke, “Matrix theory origins of non-geometric fluxes,” JHEP 1302
Original
2013
Cited alongside, same era.
D. Mylonas, P. Schupp and R. J. Szabo, “Nonassociative geometry and twist deformations in non-geometric string theory,” PoS ICMP 2013

Then

R. Blumenhagen, M. Fuchs, F. Hassler, D. Lüst and R. Sun, “Nonassociative deformations of geometry in double field theory,” JHEP 1404
Original
2014
Later among the works it cites.
D. Mylonas and R. J. Szabo, “Nonassociative field theory on non-geometric spaces,” Fortsch. Phys. 62
Original
2014
Later among the works it cites.
D. Mylonas, P. Schupp and R. J. Szabo, “Non-geometric fluxes, quasi-Hopf twist deformations and nonassociative quantum mechanics,” J. Math. Phys. 55
Original
2014
Later among the works it cites.
P. Aschieri and R. J. Szabo, “Triproducts, nonassociative ⋆ \star -products and geometry of 𝖱 \mathsf{R} -flux string compactifications,” J. Phys. Conf. Ser. 634
Original
2015
Later among the works it cites.
I. Bakas and D. Lüst, “T-duality, quotients and currents for non-geometric closed strings,” Fortsch. Phys. 63

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2016

Working with Nonassociative Geometry and Field Theory

Barnes, Gwendolyn E., Schenkel, Alexander, Szabo, Richard J.

Understand

We review aspects of our formalism for differential geometry on noncommutative and nonassociative spaces which arise from cochain twist deformation quantization of manifolds.

We work in the simplest setting of trivial vector bundles and flush out the details of our approach providing explicit expressions for all bimodule operations, and for connections and curvature.
As applications, we describe the constructions of physically viable action functionals for Yang-Mills theory and Einstein-Cartan gravity on noncommutative and nonassociative spaces, as first steps towards more elaborate models relevant to non-geometric flux deformations of geometry in closed string theory.