M2-brane near-horizon geometry (${\mathrm{AdS}}_4(R/2)\times S^7(R)$)

For $H\sim R^6/r^6$, changing radial coordinate to $z=R^3/(2r^2)$ gives an AdS metric of radius $R/2$ times a round sphere of radius $R$. The Freund-Rubin compactification flux has magnitude $6/R$ in the AdS volume form. This is the regular positive-charge membrane throat, rather than the limit of an arbitrary singular harmonic multipole.

// Target: supersymmetry.bigb