Impact of hypermultiplet higher-derivative terms on truncation consistency

Ascertain whether higher-derivative operators involving hypermultiplets in four-dimensional N=2 effective field theories obtained from Type IIA string theory compactified on a Calabi–Yau threefold obstruct the consistent truncation to the gravity and vector multiplet sectors used in deriving BPS black hole entropy via Wald’s prescription.

Background

The paper derives a macroscopic entropy formula for BPS black holes in 4d N=2 theories focusing on gravity and vector multiplet sectors, using higher-derivative F-terms captured by the generalized prepotential. While the two-derivative theory is known to truncate consistently, the role of hypermultiplet-dependent higher-derivative corrections is less clear.

The authors note that quantum corrections in the hypermultiplet sector are not fully determined, raising the possibility that unknown higher-derivative hypermultiplet couplings could affect the consistency of the truncation employed when computing the entropy. Clarifying this would establish whether the truncated sector suffices for the entropy computation at all orders.