Abstract
We elucidate relations between different approaches to describing the nonassociative deformations of geometry that arise in non-geometric string theory. We demonstrate how to derive configuration space triproducts exactly from nonassociative phase space star products and extend the relationship in various directions. By foliating phase space with leaves of constant momentum we obtain families of Moyal-Weyl type deformations of triproducts, and we generalize them to new triproducts of differential forms and of tensor fields. We prove that nonassociativity disappears on-shell in all instances. We also extend our considerations to the differential geometry of nonassociative phase space, and study the induced deformations of configuration space diffeomorphisms. We further develop general prescriptions for deforming configuration space geometry from the nonassociative geometry of phase space, thus paving the way to a nonassociative theory of gravity in non-geometric flux compactifications of string theory.
Highlights
We extend our considerations to the differential geometry of nonassociative phase space, and study the induced deformations of configuration space diffeomorphisms
We further develop general prescriptions for deforming configuration space geometry from the nonassociative geometry of phase space, paving the way to a nonassociative theory of gravity in non-geometric flux compactifications of string theory
We shall begin by describing the phase space model for the non-geometric R-flux background and discuss some ways in which it may be interpreted as a deformation of the geometry of configuration space
Summary
We shall begin by describing the phase space model for the non-geometric R-flux background and discuss some ways in which it may be interpreted as a deformation of the geometry of configuration space. It is natural in the lift of Type IIA string theory to M-theory in which the (closed string) boundary of an open M2-brane ending on an M5-brane in a constant C-field background gives rise to a noncommutative loop space algebra on the M5brane worldvolume [8, 23], which corresponds to the noncommutativity and nonassociativity felt by a fundamental closed string in a constant H-flux; this perspective is utilized in the formulation by [26] of closed string propagation in the non-geometric R-flux background using M2-brane degrees of freedom, as reviewed, and it connects open and closed string noncommutative geometry Another set of fundamental variables is obtained by considering the algebra Diff(M ) of (formal) differential operators on M with typical elements of the form.
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