Completeness of the Wald entropy formula in full Type IIA

Determine whether additional non-chiral higher-derivative operators and hypermultiplet-dependent couplings contribute to the entropy of BPS black holes in Type IIA Calabi–Yau compactifications, and whether the formula S_BH = π[|\mathscr{Z}|^2 + 4 Im(\Upsilon ∂_\Upsilon F(Y,\Upsilon))] is the complete result of applying Wald’s procedure in the full Type IIA theory.

Background

The entropy formula employed in the paper includes contributions from a tower of higher-derivative F-terms in the vector multiplet sector and is widely used in the literature. However, non-chiral higher-derivative couplings and hypermultiplet-dependent terms might, in principle, also contribute to the entropy.

Previous analyses suggest certain non-chiral vector-multiplet couplings vanish in the entropy, and neutral hypermultiplet additions do not affect the attractor geometry at specific orders. Nonetheless, the authors emphasize that at all orders the situation is not settled, especially given that the exact entropy may depend on hypermultiplet vevs, while the generalized prepotential entering the formula depends only on their number. Establishing completeness would resolve whether the quoted formula fully captures the macroscopic entropy in Type IIA.