Existence of G2 manifolds with large complex Chern–Simons invariant c2

Prove the existence of compact G2 holonomy manifolds whose complex Chern–Simons invariant parameter c2 in the flux-induced superpotential W=N^i z_i + c1 + i c2 can be made parametrically large, sufficient to enable scale separation in M-theory flux compactifications.

Background

The flux-stabilized M-theory vacua studied in the thesis rely on a large value of the imaginary component c2 of a complex Chern–Simons invariant to achieve scale separation (R_KK << R_AdS) and the resulting holographic spectra. Although the analysis assumes c2 >> 1 for certain G2 manifolds, a rigorous existence proof of such manifolds remains outstanding.

Establishing the existence of G2 holonomy manifolds that admit sufficiently large c2 would place the flux-stabilized construction on firmer mathematical footing and clarify the scope of achievable AdS vacua in M-theory.