Membrane sigma-models and quantization of non-geometric flux backgrounds
By D. Mylonas, P. Schupp, R. Szabo. 2012
147 citations recorded by the source corpus.
A bstractWe develop quantization techniques for describing the nonassociative geometry probed by closed strings in flat non-geometric R-flux backgrounds M . Starting from a suitable Courant sigma-model on an open membrane with target space M , regarded as a topological sector of closed string dynamics in R-space, we derive a twisted Poisson sigma- model on the boundary of the membrane whose target space is the cotangent bundle T*M and whose quasi-Poisson structure coincides with those previously proposed. We argue that from the membrane perspective the path integral over multivalued closed string fields in Q-space is equivalent to integrating over open strings in R-space. The corresponding boundary correlation functions reproduce Kontsevich’s deformation quantization formula for the twisted Poisson manifolds. For constant R-flux, we derive closed formulas for the corresponding nonassociative star product and its associator, and compare them with previous proposals for a 3-product of fields on R-space. We develop various versions of the Seiberg-Witten map which relate our nonassociative star products to associative ones and add fluctuations to the R-flux background. We show that the Kontsevich formula coincides with the star product obtained by quantizing the dual of a Lie 2-algebra via convolution in an integrating Lie 2-group associated to the T-dual doubled geometry, and hence clarify the relation to the twisted convolution products for topological nonassociative torus bundles. We further demonstrate how our approach leads to a consistent quantization of Nambu-Poisson 3-brackets.
Subfields: Applied Mathematics, Mathematical Physics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/1289a272840993840e0f06843112f00375d3b79c
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In Applied Mathematics
In Mathematical Physics
In Nuclear and High Energy Physics
Citations in the corpus
- Duality Symmetric String and M-Theory (2013, background): “Space limitations prevent us discussing in any detail a number of developments related to the contents of this chapter including21: the structure of large (finite) DFT gauge transformations [194, 195], the the matrix theory perspective of non-geometric fluxes [196, 197]; further perspectives on non-”
- Double field theory: a pedagogical review (2013, background): “The non-associative geometry probed by closed strings in flat non-geometric R-flux backgrounds has also been studied in [72] from a different perspective.”