Non-geometric fluxes, asymmetric strings and nonassociative geometry

Abstract

We study closed bosonic strings propagating both in a flat background with constant H-flux and in its T-dual configurations. We define a conformal field theory capturing linear effects in the flux and compute scattering amplitudes of tachyons, where the Rogers dilogarithm plays a prominent role. For the scattering of four tachyons, a fluxed version of the VirasoroShapiro amplitude is derived and its pole structure is analyzed. In the case of an R-flux background obtained after three T-dualities, we find indications for a nonassociative target-space structure which can be described in terms of a deformed tri-product. Remarkably, this product is compatible with crossing symmetry of conformal correlation functions. We finally argue that the R-flux background flows to an asymmetric CFT.

Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT’s

“…As before, one may perform the following field redefinition on τ (and similarly for ρ):τ 38) in which case one obtains the doubled space analogue of the twisted reduction:…”

A ten-dimensional action for non-geometric fluxes

“…Finally, it would be interesting to relateL to the non-commutative and non-associate geometry, discussed in [9,10,11], where it was conjectured that the effective action of a non-geometric closed string background is described by a non-associative version of gravity. We hope to come back to these questions in future publications.…”

Perspectives on Nonassociative Geometry

“…On a generic element L = e j i L j i ∈ hom A (V ,W ), the adjoint connection acts as 12) where in the last term we have used the R-matrix to rearrange the term Γ i i L j i so that -matrix multiplication is obvious.…”

“…In the standard T-duality orbit H → f → Q → R relating geometric and non-geometric fluxes, Q-flux backgrounds experience a noncommutative but strictly associative deformation while the purely non-geometric R-flux backgrounds witness a noncommutative and nonassociative geometry. Nonassociativity in this setting can be encoded by certain triproducts of fields on configuration space predicted by off-shell amplitudes in conformal field theory [12] and in double field theory [13], or by nonassociative -products from deformation quantization of twisted Poisson structures in the phase space formulation of nonassociative R-space [24,4,25]; the equivalence between these two approaches was demonstrated and extended in [3]. A general treatment of nonassociative -products in this context can be found in [20] (see also the contribution of V. Kupriyanov to these proceedings).…”