Triproducts, nonassociative star products and geometry of R -flux string compactifications
Triproducts, nonassociative star products and geometry of R -flux string compactifications
复制标题
R 通量弦紧致化的三积、非关联星积和几何
DOI：
10.1088/1742-6596/634/1/012004
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Aschieri P
中科院分区：
文献类型：
--
作者：
Aschieri P
我们阐明了描述非几何弦理论中出现的几何非联想变形的不同方法之间的关系。我们证明了如何从非结合相空间星积中精确地推导出构型空间三积，并在各个方向上推广了这种关系。用恒动量叶对相空间进行叶化，得到了三积的Moyal-Weyl型变形族，并将其推广到微分形式和张量场的新三积。我们证明了非结合性在壳层上消失。我们也将我们的考虑扩展到非结合相空间的微分几何，并研究了构形空间微分同态的诱导变形。我们进一步发展了由相空间的非结合几何变形位形空间几何的一般公式，从而为弦理论的非几何通量紧化中的非结合引力理论铺平了道路。
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.