Global gauge quotient of the evolving finite-dimensional sector

Determine whether the global integration constants arising in the evolving compact-leaf sector of the three-dimensional square-root Horndeski theory survive the full global gauge quotient.

Background

The paper establishes that the regular three-dimensional square-root Horndeski theories considered have no local bulk degrees of freedom, while allowing a possible finite-dimensional global sector associated with the leaf area density and its conjugate momentum. In the interacting example with G4=φ√X, G3=λX, and G2=ηX², the reduced variables evolve nontrivially on compact closed leaves.

Although this evolution provides explicit global integration constants, the authors do not determine whether those constants represent genuine physical data or are removed by the complete global gauge quotient. Resolving this issue is necessary to establish whether the candidate global sector defines a physical reduced phase space.

References

This evolution does not establish whether its global integration constants survive the full gauge quotient.

— Disformal Closure Selects 3D Scalar-Tensor Gravity without Local Bulk Modes  (2610.13150 - Nejati et al., 9 Oct 2026) in Supplemental Material, Section “An interacting example on the regular branch”