Superpotential from Black Holes

TL;DR

The paper addresses moduli stabilization in $N=2$ supersymmetric theories by exploring supersymmetric black holes with nonzero horizon area, showing that the low-energy superpotential can be tied to the graviphoton central charge ${|Z^{local}(t,\bar t, q,p)|^2}$ . By identifying electric and magnetic Fayet–Iliopoulos parameters with the black hole charges via $(E,M) = \Lambda^2 (q,p)$, the scalar potential becomes proportional to the central charge: $V(t,\bar t; q,p) \propto |Z^{local}(t,\bar t; q,p)|^2$. The attractor mechanism fixes moduli at the horizon by extremizing $|Z^{local}(t,\bar t; q,p)|^2$; at the fixed point, the potential minimum relates to entropy via $V_{\min} = \pi |Z(q,p)|^2_{\text{fix}} = S(q,p)$. Applications to axion-dilaton black holes and to APT-FGP-type models demonstrate the correspondence between the black hole central charge and the superpotential, enabling moduli stabilization in Lorentz-covariant effective theories and suggesting duality-consistent finite constructions that reflect black hole microphysics.

Abstract

BPS monopoles in N=2 SUSY theories may lead to monopole condensation and confinement. We have found that supersymmetric black holes with non-vanishing area of the horizon may stabilize the moduli in theories where the potential is proportional to the square of the graviphoton central charge. In particular, in known models of spontaneous breaking of N=2 to N=1 SUSY theories, the parameters of the electric and magnetic Fayet--Iliopoulos terms can be considered proportional to electric and magnetic charges of the dyonic black holes. Upon such identification the potential is found to be proportional to the square of the black hole mass. The fixed values of the moduli near the black hole horizon correspond exactly to the minimum of this potential. The value of the potential at the minimum is proportional to the black hole entropy.