Unitarity of the FRG ultraviolet fixed-point theory

Determine whether the continuum quantum gravity theory defined at the non-perturbative ultraviolet fixed point within the Functional Renormalization Group framework is unitary, i.e., whether the corresponding quantum theory admits a unitary time evolution consistent with reflection positivity when continued back to Lorentzian signature.

Background

The asymptotic safety scenario posits a non-perturbative ultraviolet fixed point enabling a predictive quantum theory of gravity via the Functional Renormalization Group (FRG). While many FRG studies provide evidence for such a fixed point, the unitarity of the resulting continuum theory is a critical physical requirement that is not automatically guaranteed.

By contrast, the lattice quantum gravity approach via Causal Dynamical Triangulations (CDT) is reflection positive after Wick rotation, ensuring unitary evolution upon continuation to Lorentzian signature. Establishing unitarity for the FRG-defined theory would strengthen the asymptotic safety program and clarify its relation to the CDT results.