Cosmological constant, near brane behavior and singularities

Abstract

We show that the classical cosmological constant in type II flux compactifications can be written as a sum of terms from the action of localized sources plus a specific contribution from non-trivial background fluxes. Exploiting two global scaling symmetries of the classical supergravity action, we find that the flux contribution can in many interesting cases be set to zero such that the cosmological constant is fully determined by the boundary conditions of the fields in the near-source region. This generalizes and makes more explicit previous arguments in the literature. We then discuss the problem of putting D3-branes at the tip of the Klebanov-Strassler throat glued to a compact space in type IIB string theory so as to engineer a de Sitter solution. Our result for the cosmological constant and a simple global argument indicate that inserting a fully localized and backreacting D3-brane into such a background yields a singular energy density for the NSNS and RR 3-form field strengths at the D3-brane. This argument does not rely on partial smearing of the D3-brane or a linearization of field equations, but on a few general assumptions that we also discuss carefully.

Giant tachyons in the landscape

“…This implies that the quadratic term in the polarization potential for this channel vanishes, 8 and hence we have:…”

“…This intuition was challenged by the fact that the supergravity solution describing backreacting anti-D3 branes in the Klebanov-Strassler solution must have a certain singularity in the infrared, both when the anti-D3 branes are smeared on the S 3 at the bottom of the deformed conifold [4][5][6][7], and also when they are localized [8]. Furthermore, it was shown that this singularity cannot be cloaked with a black hole horizon [9,10], nor via polarization into D5 branes at a finite distance away from the KS tip [11].…”

Gravity and on-shell probe actions

“…Related and extremely instructive results using probe branes in holographic set-ups have also appeared in the earlier literature [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37].…”

“…27,28 The gauge potential satisfies 17) where Ω M is the volume form of M , generalizing (3.7). 29 The ambiguity in C d , coming from the integration of (3.17), produces the usual ambiguity in the probe action. Since all brane worldvolumes we consider are homologous to each other, this ambiguity is simply an overall worldvolume-independent constant in the action.…”

“…28 We can also use a non-BPS probe with actionτ A − iτ C d and BPS boundτ ≥ |τ | without changing the subsequent discussion in any important way. 29 The second term in (3.7) is irrelevant for our purposes. The precise implementation of this prescription is as follows.…”