Nonperturbative definition of quantum gravity

Develop a well-defined, nonperturbative formulation of quantum gravity that does not rely on perturbation theory in the Newton constant (i.e., beyond graviton-loop expansions).

Background

In discussing how classical results might extend to quantum gravity, the paper highlights a fundamental limitation: current formulations are mainly perturbative in the Newton constant and rely on graviton-loop expansions. This restriction motivates looking for a nonperturbative definition that could underpin a robust notion of quantum subsystems and their algebras.

The author notes that while perturbative algebraic approaches (e.g., pAQFT with BV-BRST) provide local field algebras around fixed backgrounds, a fully nonperturbative construction remains absent. A solution to this problem would enable a more complete and background-independent framework for gravitational subsystems.

References

For one thing, it is not known how to define quantum gravity outside of perturbation theory in the Newton constant, which is equivalent to an expansion in graviton loops.

— Dressed Subsystems in Classical Gravity  (2501.10450 - Pulakkat, 14 Jan 2025) in Section 5.3 (Prospects for Quantization)

It is an interesting and open question as to whether lattice field theory approaches may be used to formulate quantum gravity.

— Evidence of Taste-Symmetry restoration for Kähler-Dirac fermions on Euclidean Dynamical Triangulations  (2610.13791 - Dai et al., 9 Oct 2026) in Section I, Introduction