Nonassociative modifications of general relativity, GR, and quantum gravity, QG, models naturally arise as star product and R-flux deformations considered in string/M-theory. Such nonassociative and noncommutative geometric and quantum information theories were formulated on phase spaces defined as cotangent Lorentz bundles enabled with nonassociative symmetric and nonsymmetric metrics and nonlinear and linear connection structures. We outline the analytic methods and proofs that corresponding geometric flow evolution and dynamical field equations can be decoupled and integrated in certain general off-diagonal forms. New classes of solutions describing nonassociative black holes, wormholes, and locally anisotropic cosmological configurations are constructed using such methods. We develop the Batalin–Vilkovisky, BV, formalism for quantizing modified gravity theories, MGTs, involving twisted star products and semi-classical models of nonassociative gauge gravity with de Sitter/affine/ Poincaré double structure groups. Such theories can be projected on Lorentz spacetime manifolds in certain forms equivalent to GR or MGTs with torsion generalizations etc. We study the properties of the classical and quantum BV operators for nonassociative phase spaces and nonassociative gauge gravity. Recent results and methods from algebraic QFT are generalized to involve nonassociative star product deformations of the anomalous master Ward identity. Such constructions are elaborated in a nonassociative BV perspective and for developing non-perturbative methods in QG.

中文翻译：

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代数量子场论中具有 R 通量星星积和 Batalin-Vilkovisky 量子化的非关联规范引力理论


广义相对论 GR 和量子引力 QG 模型的非结合修改自然而然地作为星积和 R 磁通量变形出现，在弦/M 理论中考虑。这种非结合和非交换几何和量子信息理论是在相空间上制定的，相空间定义为余切洛伦兹束，具有非结合对称和非对称度量以及非线性和线性连接结构。我们概述了相应的几何流演化和动态场方程可以解耦并集成在某些一般非对角线形式的解析方法和证明。描述非结合黑洞、虫洞和局部各向异性宇宙构型的新解就是用这些方法构建的。我们开发了 Batalin-Vilkovisky， BV，用于量化修正引力理论 MGT 的形式主义，涉及扭曲星积和非关联规范引力的半经典模型，具有 de Sitter/affine/Poincaré 双结构群。这样的理论可以以某种形式投影到洛伦兹时空流形上，相当于 GR 或 MGT，具有扭转泛化等。我们研究了非关联相空间和非关联规范引力的经典和量子 BV 算子的性质。代数 QFT 的最新结果和方法被推广为涉及异常主 Ward 恒等式的非结合星积变形。这种结构以非结合 BV 的角度进行阐述，并用于在 QG 中开发非扰动方法。