### 11/06/2013, 16:30 — 17:00 — Room P3.10, Mathematics Building

Richard Szabo, *Heriot-Watt University Edinburgh*

### Quantization of non-geometric flux backgrounds

We describe the emergence of nonassociative geometries 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 membranes propagating in the
phase space of the target space compactification. Quantization of
the membrane sigma-model leads to a proper quantization of the
nonassociative background, which we relate to Kontsevich's
formalism of global deformation quantization. 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 and cochain
twist quantization using suitable quasi-Hopf algebras.

#### See also

http://www.math.ist.utl.pt/~jmourao/strings/20130611_Szabo_slides.pdf