Localised Anti-Branes in Flux Backgrounds

TL;DR

This work demonstrates that localised anti-branes in flux backgrounds admit finite-temperature backreacted solutions of both charges, with horizon shielding indicating the singularities are physical and resolvable within string theory. The authors adapt the KPV framework to a KS-like toy background and find that localised branes yield stable configurations at finite temperature, while extremal anti-branes drive horizon flux to divergent values that are plausibly cured by brane polarisation in a non-supersymmetric Polchinski-Strassler setup. The results challenge claims that anti-brane singularities invalidate metastable SUSY-breaking states or the de Sitter landscape, especially once smearing is avoided. The work thus supports the existence of metastable non-SUSY states and highlights a promising polarisation mechanism, while outlining the need for higher-order analysis and a full non-linear construction to confirm the proposed resolutions. It also notes that the no-go results for smeared cases do not necessarily apply to fully localised configurations, suggesting a more nuanced understanding of horizons in flux backgrounds.

Abstract

Solutions corresponding to finite temperature (anti)-D3 and M2 branes localised in flux backgrounds are constructed in a linear approximation. The flux backgrounds considered are toy models for the IR of the Klebanov-Strassler solution and its M-theory analogue, the Cvetič-Gibbons-Lü-Pope solution. Smooth solutions exist for either sign charge, in stark contrast with the previously considered case of smeared black branes. That the singularities of the anti-branes in the zero temperature extremal limit can be shielded behind a finite temperature horizon indicates that the singularities are physical and resolvable by string theory. As the charge of the branes grows large and negative, the flux at the horizon increases without bound and diverges in the extremal limit, which suggests a resolution via brane polarisation à la Polchinski-Strassler. It therefore appears that the anti-brane singularities do not indicate a problem with the SUSY-breaking metastable states corresponding to expanded anti-brane configurations in these backgrounds, nor with the use of these states in constructing the de Sitter landscape.

Figures (7)

• Figure 1: $p/M = 0.01, 0.03, 0.04, 0.07, 0.09$, from bottom to top. Metastable minima exist for $p/M \lesssim 0.08$, and are indicated by black dots.
• Figure 2: The probe potential $\Phi$ for $p/\mu=1$. The global minima is indicated by a black dot. The key differences between the potential for the KS background and the toy flux background \ref{['eq:IIBflux']} are that the minima corresponding to an NS5 brane wrapping a finitely sized $S^2$ is 1) always present for the toy flux background, and 2) always the global minima as opposed to simply a metastable minima.
• Figure 3: The perturbation function $g_4$ for $\beta = 1$ and $\varepsilon = 1$ (lower curve) and $\varepsilon = -1$ (upper curve). Note that the flux at the horizon, $(r_+/r)^4 = 1$, is significantly larger for the anti-aligned $\varepsilon = -1$ case.
• Figure 4: The value of the rescaled perturbation $g_+$ at the horizon. As extremality is approached, the flux either vanishes $(\varepsilon = 1)$, or diverges $(\varepsilon = -1)$. Recall that our convention is that $\beta\ge 0$ always. Fitting the data indicates that $g_+(r_+) \sim e^{\beta/2}$ as $\beta \rightarrow \infty$ for $\varepsilon = -1$, which corresponds to $g_4(r_+) \sim e^{2\beta}$.
• Figure 5: Schematic depiction of the proposed supergravity solution corresponding to anti-D3 branes in the Klebanov-Strassler solution. The solution interpolates between a Klebanov-Strassler throat asymptotically, and a mass-deformed $AdS_5 \times S^5$ throat. The $\Delta =1$ mode of the $G_3$ flux grows down the throat, until it eventually induces polarisation, leading to the (as yet un-constructed) backreacted non-supersymmetric Polchinski-Strassler solution. It should be noted that each throat has a distinct radial coordinate.