Superpotential from Black Holes

TL;DR

This paper explores how supersymmetric black holes can stabilize moduli in N=2 SUSY theories, linking black hole properties to potential minimization and entropy, with implications for confinement mechanisms.

Contribution

It demonstrates that black hole horizons can stabilize moduli in N=2 SUSY theories and relate the potential's minimum to black hole entropy, revealing a novel connection between black holes and field theory vacua.

Findings

Black hole horizon stabilizes moduli at potential minimum.

Potential proportional to black hole mass squared.

Potential at minimum proportional to black hole entropy.

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.