Matrix theory origins of non-geometric fluxes

Abstract

We explore the origins of non-geometric fluxes within the context of M theory described as a matrix model. Building upon compactifications of Matrix theory on non-commutative tori and twisted tori, we formulate the conditions which describe compactifications with non-geometric fluxes. These turn out to be related to certain deformations of tori with non-commutative and nonassociative structures on their phase space. Quantization of flux appears as a natural consequence of the framework and leads to the resolution of nonassociativity at the level of the unitary operators. The quantum-mechanical nature of the model bestows an important role on the phase space. In particular, the geometric and non-geometric fluxes exchange their properties when going from position space to momentum space thus providing a duality among the two. Moreover, the operations which connect solutions with different fluxes are described and their relation to T-duality is discussed. Finally, we provide some insights on the effective gauge theories obtained from these matrix compactifications.

(Non-)commutative closed string on T-dual toroidal backgrounds

“…3 Approaches using dual membrane theories [30] and matrix models [31] arrive at the same conclusion.…”

Extended geometry and gauged maximal supergravity

“…Some definitions and results for d < 6 are given in [27], and some more for d = 4, 5 in [42]. Finally, for completion we provide a list of complementary results along these lines [43][44][45]- [51].…”

Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids

“…After formally applying a third T-duality, not along an isometry direction anymore, one arrives at an R-flux background which does not admit a clear target-space interpretation. This chain of T-duality transformations can be summarized as [4] H abc For the non-geometric R-flux, it has been argued both from a non-commutative geometry [5,6,7] and from a conformal field theory [8,9,10,11] point of view that a non-associative structure is induced. However, in contrast to the wellestablished non-commutative behavior of open strings [12], the generalization of non-commutativity and non-associativity to the closed string sector is more difficult, since in a gravitational theory the non-commutativity parameter is expected to be dynamical.…”