Microscopic explanation of the square-root rescaling in brane counting

Determine whether a microscopic mechanism explains the replacement of the naive brane-counting parameter by the square-root scaling n\mapsto N^{1/2} required to reproduce the flux-vacuum parametric exponents.

Background

The naive independent-brane counting gives central-charge and field-scaling exponents that differ from those of the actual flux vacuum. The two sets of exponents can be related formally by replacing the brane-counting parameter n with N^{1/2}, where N is the quantized F4-flux parameter. Because the branes are correlated by tadpole cancellation and Freed–Witten constraints, the authors do not know whether this rescaling has a genuine microscopic origin or is merely coincidental.