Nonassociative gauge gravity theories with R-flux star products and Batalin–Vilkovisky quantization in algebraic quantum field theory

Abstract

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.