Asymptotic safe nonassociative quantum gravity with star R-flux products, Goroff-Sagnotti counter-terms, and geometric flows

TL;DR

This paper demonstrates that nonassociative modifications of general relativity, involving R-flux deformations, can be formulated as viable quantum gravity theories through generalized asymptotic safety and geometric flow techniques.

Contribution

It introduces a new nonholonomic functional renormalization approach for nonassociative quantum gravity with R-flux deformations, establishing their consistency and viability.

Findings

Nonassociative gravity theories can be well-defined as classical and quantum models.

Generalized G. Perelman thermodynamic variables are computed for nonassociative flows.

Effective models with off-diagonal solutions support asymptotic safety in nonassociative QG.

Abstract

Nonassociative modifications of general relativity, GR, defined by star products with R-flux deformations in string gravity consist of an important subclass of modified gravity theories, MGTs. A longstanding criticism for elaborating quantum gravity, QG, argue that the asymptotic safety does not survive once certain perturbative terms (in general, nonassociative and noncommutative) are included in the projection space. The goal of this work is to prove that a generalized asymptotic safety scenario allows us to formulate physically viable nonassociative QG theories using effective models defined by generic off-diagonal solutions and nonlinear symmetries in nonassociative geometric flow and gravity theories. We elaborate on a new nonholonomic functional renormalization techniques with parametric renormalization group, RG, flow equations for effective actions supplemented by certain canonical two-loop counter-terms. The geometric constructions and quantum deformations are performed for nonassociative phase spaces modelled as R-flux deformed cotangent Lorentz bundles. Our results prove that theories involving nonassociative modifications of GR can be well defined both as classical nonassociative MGTs and QG models. Such theories are characterized by generalized G. Perelman thermodynamic variables which are computed for certain examples of nonassociative geometric and RG flows.