Describe boundary conditions for multiple-collapse data of CFTs

Determine the general differential-geometric conditions, including the required equations on fiber metrics and additional structures such as non-linear connections, that the tower of fibrations and associated metric data must satisfy to describe boundary points of the compactified moduli space arising from multiple collapses of Conformal Field Theories.

Background

Boundary points after multiple collapse are described by towers of fibrations with metrics on fibers, bounded diameters, and maps into lower-central-charge moduli components, along with extra geometric data (e.g., non-linear connections).

Although the qualitative structure is described, the precise analytic and geometric conditions (e.g., differential equations governing the metrics and connections) are unspecified; characterizing them is essential for a comprehensive boundary theory.