Generalization of the Wick-rotated holomorphic framework beyond the CSK state

Investigate whether the combination of the holomorphic inner product for self-dual gravity and a mode-selective Thiemann phase-space Wick rotation can be generalized beyond the Chern–Simons–Kodama state to construct normalizable vacuum wavefunctionals in nonperturbative quantum gravity with positive cosmological constant.

Background

The authors show that, with the holomorphic inner product, the linearized CSK state is perturbatively normalizable for super-Planckian Λ, and propose a phase-space Wick rotation (in the spirit of Thiemann’s complexifier) to render the perturbative norm finite at sub-Planckian Λ by analytically continuing only the divergent modes.

They then speculate that this combined strategy might extend beyond the CSK state to provide a general template for constructing viable vacuum states in nonperturbative quantum gravity with Λ>0, explicitly formulating this expectation as a conjecture.