Ricci-flat manifolds as targets of degenerating CFTs

Show that every compact Ricci-flat manifold, with its metric defined up to a positive scalar multiple, arises as the target space of a degenerating family of Conformal Field Theories.

Background

In the collapse picture of CFTs, sigma models on target manifolds appear near boundary strata of the compactified moduli space. For purely bosonic sigma models, the target metric is Ricci flat in the simplest case.

The conjecture posits a comprehensive realization: all compact Ricci-flat manifolds occur as such limits, framing geometric compactification problems (Einstein manifolds) within the CFT degeneration paradigm.