Quantum black hole entropy and the holomorphic prepotential of N=2 supergravity

Understand

Supersymmetric terms in the effective action of N=2 supergravity in four dimensions are generically classified into chiral-superspace integrals and full-superspace integrals.

• For a theory of N=2 vector multiplets coupled to supergravity, a special class of couplings is given by chiral-superspace integrals that are governed by a holomorphic prepotential function.
• The quantum entropy of BPS black holes in such theories depends on the prepotential according to a known integral formula.
• We show, using techniques of localization, that a large class of full-superspace integrals in the effective action of N=2 supergravity do not contribute to the quantum entropy of BPS black holes at any level in the derivative expansion.