Non-Supersymmetric Attractors in String Theory

TL;DR

This work extends the attractor mechanism to non-supersymmetric extremal black holes in ${ m N}=2$ Type II string theory. By formulating the problem in terms of the vector-multiplet effective potential $V_{eff}$ and analyzing its critical points and Hessian, the authors identify conditions under which non-supersymmetric attractors exist: at large volume in Type IIA without D6 branes, a non-supersymmetric attractor can arise with a positive quartic correction along zero-mode directions; with D6 branes, a supersymmetry-breaking extremum can occur but fails to be an attractor due to cubic leading corrections. They also study the mirror IIB description of the quintic near the Gepner point, showing non-supersymmetric attractors can exist in that regime for suitable charges, with explicit entropy and mass-spectrum details and a consistent microscopic interpretation of entropy. Overall, the paper demonstrates that non-supersymmetric attractors are robust in certain regions of moduli space, while the presence of D6 branes and the structure of zero modes critically determine attractor behavior and stability.

Abstract

We find examples of non-supersymmetric attractors in Type II string theory compactified on a Calabi Yau three-fold. For a non-supersymmetric attractor the fixed values to which the moduli are drawn at the horizon must minimise an effective potential. For Type IIA at large volume, we consider a configuration carrying D0, D2, D4 and D6 brane charge. When the D6 brane charge is zero, we find for some range of the other charges, that a non-supersymmetric attractor solution exists. When the D6 brane charge is non-zero, we find for some range of charges, a supersymmetry breaking extremum of the effective potential. Closer examination reveals though that it is not a minimum of the effective potential and hence the corresponding black hole solution is not an attractor. Away from large volume, we consider the specific case of the quintic in CP^4. Working in the mirror IIB description we find non-supersymmetric attractors near the Gepner point.

Figures (1)

• Figure 1: Plot for the field $\delta\phi\left({r-r_H\over r_H}\right)$ as a function of $\left({r-r_H\over r_H}\right)$ for different values of $c$. Here we have chosen $\lambda = 1$ and $r_H = 2$. The integration constant $c$ takes values $0.1,0.2\cdots 1.0$. The solution is interpolated from ${r-r_H\over r_H} = e^{-50}$ to ${r-r_H\over r_H} = e^3$.