Magnetic Backgrounds and Noncommutative Field Theory

“…The emergent noncommutative geometry in this limit is completely analogous to that of electron coordinates in a constant magnetic background in the lowest Landau level (see e.g. [65]). …”

Section: String Geometrymentioning

confidence: 91%

Nonassociative geometry and twist deformations in non-geometric string theory

Mylonas¹,

Schupp²,

Szabo

2014

Proceedings of Third International Satellite Conference on Mathematical Methods in Physics — PoS(ICMP 2013)

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We describe nonassociative deformations of geometry probed by closed strings in non-geometric flux compactifications of string theory. We show that these non-geometric backgrounds can be geometrised through the dynamics of open membranes whose boundaries propagate in the phase space of the target space compactification, equiped with a twisted Poisson structure. The effective membrane target space is determined by the standard Courant algebroid over the target space twisted by an abelian gerbe in momentum space. Quantization of the membrane sigma-model leads to a proper quantization of the non-geometric background, which we relate to Kontsevich's formalism of global deformation quantization that constructs a noncommutative nonassociative star product on phase space. We construct Seiberg-Witten type maps between associative and nonassociative backgrounds, and show how they may realise a nonassociative deformation of gravity. We also explain how this approach is related to the quantization of certain Lie 2-algebras canonically associated to the twisted Courant algebroid, and cochain twist quantization using suitable quasi-Hopf algebras of symmetries in the phase space description of R-space which constructs a Drinfel'd twist with non-trivial 3-cocycle. We illustrate and apply our formalism to present a consistent phase space formulation of nonassociative quantum mechanics.

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“…3 If the external legs carry momentum p, then the planar tadpole diagram gives the momentum space Feynman integral…”

Section: Renormalization Scalar Field Theorymentioning

confidence: 99%