Quantum Lift of Non-BPS Flat Directions

TL;DR

This paper investigates quantum corrections to the attractor equations in N=2, d=4 supergravity, revealing that certain flat directions persist and acquire non-zero axion values in the presence of D0-D6 branes, unlike classical solutions.

Contribution

It demonstrates that quantum corrections preserve some flat directions in the black hole potential and show how these directions evolve with different brane configurations.

Findings

Flat directions persist with quantum corrections in D0-D6 branes.

Solutions develop non-zero axion fields due to quantum effects.

Classical flat directions reduce to critical points with zero axion in other brane cases.

Abstract

We study N=2, d=4 attractor equations for the quantum corrected two-moduli prepotential $\mathcal{F}=st^2+i\lambda$, with $\lambda$ real, which is the only correction which preserves the axion shift symmetry and modifies the geometry. In the classical case the black hole effective potential is known to have a flat direction. We found that in the presence of D0-D6 branes the black hole potential exhibits a flat direction in the quantum case as well. It corresponds to non-BPS $Z\neq 0$ solutions to the attractor equations. Unlike the classical case, the solutions acquire non-zero values of the axion field. For the cases of D0-D4 and D2-D6 branes the classical flat direction reduces to separate critical points which turn out to have a vanishing axion field.