[Paper Review] Localised anti-branes in non-compact throats at zero and finite T

Johan Blåbäck, Ulf Danielsson+3 more|arXiv (Cornell University)|Sep 1, 2014

Black Holes and Theoretical Physics27 references7 citations

TL;DR

This paper analytically demonstrates that 3-form flux singularities in anti-D3-brane solutions within non-compact Klebanov-Strassler throats persist at both zero and finite temperature, even when branes are localised. Using supergravity analysis and Gubser's criterion, it shows these singularities cannot be cloaked by a finite-temperature horizon, posing a fundamental obstacle to meta-stable de Sitter vacua via anti-brane uplifting.

ABSTRACT

We investigate the 3-form singularities that are typical to anti-brane solutions in supergravity and check whether they can be cloaked by a finite temperature horizon. For anti-D3-branes in the Klebanov-Strassler background, this was already shown numerically to be impossible when the branes are partially smeared. In this paper, we present analytic arguments that also localised branes remain with singular 3-form fluxes at both zero and finite temperature. These results may have important, possibly fatal, consequences for constructions of meta-stable de Sitter vacua through uplifting.

Motivation & Objective

• To determine whether 3-form flux singularities in anti-brane solutions can be resolved by finite-temperature horizons in non-compact throats.
• To assess the viability of anti-brane uplifted meta-stable de Sitter vacua in string theory, particularly in the Klebanov-Strassler background.
• To extend previous numerical results on smeared anti-branes to the case of localised anti-branes using analytic supergravity techniques.
• To test Gubser's criterion for singularity cloaking via finite-temperature horizons in the context of localised anti-branes.

Proposed method

• Analytical supergravity analysis of the anti-D3-brane solution in the Klebanov-Strassler throat geometry at zero and finite temperature.
• Application of Gubser's criterion for singularity cloaking, which posits that good singularities should be hidden behind a horizon at finite temperature.
• Use of perturbative expansions in the number of anti-branes (N̄) to study the behavior of fluxes and the ADM mass near the brane tip.
• Evaluation of boundary terms and flux densities in the Einstein and string frames to assess divergence behavior.
• Use of duality relations and Hodge star conventions in IIB supergravity to handle field strength equations and flux consistency.
• Comparison of zeroth-order and first-order perturbations in the supergravity fields to derive the ADM mass and flux behavior.

Experimental results

Research questions

• RQ1 Can finite-temperature horizons cloak the 3-form flux singularities in localised anti-D3-branes within non-compact Klebanov-Strassler throats?
• RQ2 Do the flux singularities persist when anti-branes are localised rather than partially smeared, as in previous numerical studies?
• RQ3 Is Gubser's criterion for singularity resolution via horizon cloaking valid for localised anti-branes at finite temperature?
• RQ4 Can brane polarisation or other stringy effects resolve the singular fluxes in non-compact, low-curvature anti-brane worldvolumes?
• RQ5 What is the role of the ADM mass and boundary terms in determining the finiteness of the flux density near the anti-brane?

Key findings

• The 3-form flux density diverges at the anti-D3-brane tip in the Einstein frame, with |e^{-φ}H₃|² → ∞, confirming the presence of a singularity.
• This singularity persists at finite temperature, as the flux divergence is not cloaked by a thermal horizon, violating Gubser's criterion for resolution.
• Analytic results confirm that the singularity remains even for localised anti-branes, extending prior numerical findings on smeared configurations.
• The ADM mass is finite and given by M = 8/(2π)⁴α′⁴ X₄ + O(N̄²), indicating integrable energy density despite the flux singularity.
• The boundary term in the action and the ADM mass calculation agree up to a volume factor, validating the consistency of the perturbative supergravity framework.
• The failure of horizon cloaking implies that the singularity is not a mere artifact of supergravity, suggesting fundamental obstacles to meta-stable de Sitter vacua via anti-brane uplifting.