Non-associative differential geometry and L algebras towards a description of non-geometric closed string vacua

由弦论的局部非几何R通量背景诱导的非结合引力的基础在[1]中奠定。沿着同一方向，我们研究了我们几何时空上非结合微分同胚下的不变性关系、闭弦理论的经典微分同胚对称性和双场论的广义微分同胚对称性。此外，我们的目标是构造一个适当的作用泛函的非结合爱因斯坦方程，并进一步研究的拉回相空间扭曲和黎曼曲率的基础时空。为了达到这个目标，我们将用L代数的语言来表示爱因斯坦-嘉当引力，就像最近对通常的规范理论所做的那样[2]。接下来，我们的目标是扭曲潜在的几何结构。这一系列的研究应该为非结合几何作为闭弦理论的低能量极限的预期相关性提供证据

The foundations of a non-associative gravity induced by locally non-geometric R-flux backgrounds of string theory were laid in [1]. Moving on the same direction, we study the relation of invariance under non-associative diffeomorphisms on spacetime of our geometry, the classical diffeomorphism symmetry of closed string theory and the generalized diffeomorphism symmetries of double field theory. Furthermore, we aim to construct an appropriate action functional for the on-associative Einstein equations, and further study the pullbacks of phase space Torsion and Riemann curvatures to the underlying spacetime. Towards this goal we shall express Einstein-Cartan gravity in the language of L algebras, as done recently for usual gauge theories [2]. Following that, we aim to twist the underlying geometrical structure. This line of research should provide evidence for the expected relevance of non associative geometry as a low energy limit of closed string theory