Nonlinear intrinsic DFT holographic counterterms

Establish a general nonlinear, intrinsic, and O(D,D)-covariant boundary-counterterm completion that renormalizes the holographic action beyond quadratic order about the non-Riemannian vacuum and remains applicable to generic states.

Background

The supplemental material constructs quadratic source counterterms for the Riemannian and non-Riemannian branches and compares them with an intrinsic boundary-curvature candidate. The intrinsic candidate reproduces the required divergences through quadratic order about the vacuum, up to total derivatives and finite local adjustments.

For generic nonzero L_+ and L_-, the candidate leaves uncanceled divergences. A fully nonlinear counterterm functional that is intrinsic to the boundary and covariant under O(D,D) is therefore still missing.