Nonassociative Tori and Applications to T-Duality

Bouwknegt, Peter; Hannabuss, K. C.; Mathai, Varghese

doi:10.1007/s00220-005-1501-8

Cited by 116 publications

(235 citation statements)

References 39 publications

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“…Then the Buscher rules [34] allow one to T-dualize along either the y or z directions, resulting in metric flux ω y xz or ω z xy , or T-dualize in y and z, resulting in Q yz x , but it is not obvious how to perform the third T-duality here to get R xyz ; our trivialization broke the third isometry, and the Buscher rules no longer apply. Indeed, there are general arguments that any tendimensional origin for R-flux cannot even have a local description [6,35]. So it is very much of interest to ask which configurations can be constructed from ten dimensions.…”

Section: Summary and Puzzlesmentioning

confidence: 99%

Toroidal orientifolds in IIA with general NS-NS fluxes

Ihl

Robbins

Wrase

2007

J. High Energy Phys.

184

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Type IIA toroidal orientifolds offer a promising toolkit for model builders, especially when one includes not only the usual fluxes from NS-NS and R-R field strengths, but also fluxes that are T-dual to the NS-NS three-form flux. These new ingredients are known as metric fluxes and non-geometric fluxes, and can help stabilize moduli or can lead to other new features. In this paper we study two approaches to these constructions, by effective field theory or by toroidal fibers twisted over a toroidal base. Each approach leads us to important observations, in particular the presence of D-terms in the four-dimensional effective potential in some cases, and a more subtle treatment of the quantization of the general NS-NS fluxes. Though our methods are general, we illustrate each approach on the example of an orientifold of T 6 /Z 4 .

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Section: Summary and Puzzlesmentioning

confidence: 99%

Toroidal orientifolds in IIA with general NS-NS fluxes

Ihl

Robbins

Wrase

2007

J. High Energy Phys.

184

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“…In [13], [14] the case of principle torus bundles was discussed. Dimensional reduction of H on the T d fibres gives forms H 3 , H 2 , H 1 , H 0 where H p is a p-form on the base.…”

Section: Introductionmentioning

confidence: 99%

Global aspects of T-duality, gauged sigma models and T-folds

Hull

2007

J. High Energy Phys.

116

205

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The gauged sigma-model argument that string backgrounds related by T-dual give equivalent quantum theories is revisited, taking careful account of global considerations. The topological obstructions to gauging sigma-models give rise to obstructions to Tduality, but these are milder than those for gauging: it is possible to T-dualise a large class of sigma-models that cannot be gauged. For backgrounds that are torus fibrations, it is expected that T-duality can be applied fibrewise in the general case in which there are no globally-defined Killing vector fields, so that there is no isometry symmetry that can be gauged; the derivation of T-duality is extended to this case. The T-duality transformations are presented in terms of globally-defined quantities. The generalisation to non-geometric string backgrounds is discussed, the conditions for the T-dual background to be geometric found and the topology of T-folds analysed.

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“…The cochain twist deformation quantization techniques originally developed by [25] were motivated by the search for a systematic way to generalize notions of differential geometry to such non-geometric backgrounds, and in particular to construct nonassociative deformations of field theory and ultimately gravity (see also [3]); this approach is different in spirit to the nonassociative twist deformation of the geometric f-flux frame considered in [18], which does not seem to be of relevance for non-geometric string theory, nor does it agree with the string theory inspired nonassociative torus bundles of [14,19] which reproduce the classical limit only up to Morita equivalence. Physically consistent models with novel properties in the context of quantum mechanics were constructed in [25] using this formalism, and of Euclidean scalar quantum field theory in [23].…”

Section: G E Barnes a Schenkel And R J Szabomentioning

confidence: 99%

Perspectives on Nonassociative Geometry

Szabo¹,

Barnes²,

Schenkel³

2016

Proceedings of Proceedings of the Corfu Summer Institute 2015 — PoS(CORFU2015)

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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.

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Nonassociative Tori and Applications to T-Duality

Cited by 116 publications

References 39 publications

Toroidal orientifolds in IIA with general NS-NS fluxes

Toroidal orientifolds in IIA with general NS-NS fluxes

Global aspects of T-duality, gauged sigma models and T-folds

Perspectives on Nonassociative Geometry

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