Horizons cannot save the Landscape

TL;DR

This work tests the proposal that anti-D3 brane singularities in KS/KT backgrounds could be physical if cloaked by a horizon, by analyzing Klebanov-Tseytlin and mass-deformed Klebanov-Strassler black holes. The authors show that horizon D3-charge $Q_b^{D3}$ is constrained by the asymptotic charge and thermodynamic data, with KT black holes yielding $Q_b^{D3}=rac{1}{27\pi} k_0^h>0$ and KS mass-deformed black holes remaining positive for the explored parameter space. Consequently, there is no black hole with opposite-sign horizon charge to cloak the singularity, suggesting anti-brane singularities are unphysical and challenging de Sitter uplifts based on anti-branes in these backgrounds. Moreover, the horizon charge is not an independent parameter; it is determined by the temperature and gaugino masses, indicating that adding an antibrane would provoke charge exchange with flux and potential instability rather than stabilization. The results constrain the string theory landscape in these settings and motivate exploring alternative uplift mechanisms or broader parameter regions with improved numerics.

Abstract

Solutions with anti-D3 branes in a Klebanov-Strassler geometry with positive charge dissolved in fluxes have a certain singularity corresponding to a diverging energy density of the RR and NS-NS three-form fluxes. There are many hopes and arguments for and against this singularity, and we attempt to settle the issue by examining whether this singularity can be cloaked by a regular event horizon. This is equivalent to the existence of asymptotically Klebanov-Tseytlin or Klebanov-Strassler black holes whose charge measured at the horizon has the opposite sign to the asymptotic charge. We find that no such KT solution exists. Furthermore, for a large class of KS black holes we considered, the charge at the horizon must also have the same sign as the asymptotic charge, and is completely determined by the temperature, the number of fractional branes and the gaugino masses of the dual gauge theory. Our result suggests that antibrane singularities in backgrounds with charge in the fluxes are unphysical, which in turn raises the question as to whether antibranes can be used to uplift AdS vacua to deSitter ones. Our results also point out to a possible instability mechanism for the antibranes.

Figures (8)

• Figure 1: Left Panel: The dimensionless temperature $\frac{T}{\Lambda}$ as a function of the microscopic parameter $k_s$. The inset plot zooms it in the neighbourhood of $T=T_u$ (green point). The red dots correspond to $k_s\le k_{u}$ and the blue dots correspond to $k_s\ge k_{u}$. To the left of the last red dot there are no black holes. Right Panel: The Kretschmann scalar at the horizon as a function of the microscopic parameter $k_s$.
• Figure 2: Left Panel: The dimensionless energy density as a function of the dimensionless temperature. The inset plot shows this energy in the vicinity of the onset of the perturbative instability of the cascading plasma (where $T=T_u$, the green point). Right Panel: The dimensionless free energy density as a function of the temperature for temperatures at the deconfinement transition ($T=T_c$; magenta point) and around it. The inset plot shows the free energy density in the vicinity of the perturbative instability of the cascading plasma ($T=T_u$; green point) and all the way down to the last red point that represents the last KT black hole that exists. In these figures, the red/blue dots have the same meaning as in Fig. \ref{['figure1']}.
• Figure 3: Left Panel: The dimensionless entropy density as a function of the dimensionless energy density in the vicinity of $T=T_u$. Right Panel: Square of speed of sound $c_s^2$ in the vicinity of $T=T_u$.
• Figure 4: The dimensionless D3-brane charge of the black hole $Q_b^{D3}$ as a function of the dimensionless temperature.
• Figure 5: Mobile D3-brane charge $Q_b^{D3}$ for mass-deformed KS black holes with mass-deformation parameters $f_{a10}=0.1$ and $k_{110}=0$, as a function of $k_s$ (related to $T/\Lambda$).