Compactness and deformation dimension of the CFT moduli stack

Prove that the moduli stack M_{c≤c0}^{E_min} of irreducible unitary Conformal Field Theories with central charge c≤c0 and minimal positive conformal dimension at least E_min is a compact real-analytic stack of finite local dimension, and determine that the base of the miniversal deformation of any given CFT has dimension at most dim H^{1,1}.

Background

The paper considers CFTs with bounded central charge and a lower bound on the minimal positive eigenvalue of L_0+L̄0 (the spectral gap). The proposed moduli object M{c≤c0}^{E_min} is expected to have good analytic and compactness properties.

Bounding the local dimension of the miniversal deformation base by dim H^{1,1} reflects a specific cohomological control over deformations within the CFT framework.