The backreaction of anti-D3 branes on the Klebanov-Strassler geometry

Abstract

We present the full numerical solution for the 15-dimensional space of linearized deformations of the Klebanov-Strassler background which preserve the SU(2) X SU(2) X Z_2 symmetries. We identify within this space the solution corresponding to anti-D3 branes, (modulo the presence of a certain subleading singularity in the infrared). All the 15 integration constants of this solution are fixed in terms of the number of anti-D3 branes, and the solution differs in the UV from the supersymmetric solution into which it is supposed to decay by a mode corresponding to a rescaling of the field theory coordinates. Deciding whether two solutions that differ in the UV by a rescaling mode are dual to the same theory is involved even for supersymmetric Klebanov-Strassler solutions, and we explain in detail some of the subtleties associated to this.Comment: 41 pages, 5 figures, LaTe

Inflation and String Theory

“…If one could establish that the corresponding full, exact solution manifests unphysical singularities, this would imply that anti-D3-branes in a KS throat do not provide a consistent metastable supersymmetry-breaking configuration. To discuss this important point [427][428][429][430][431][432][433][434][435][436][437][438][439][440][441], we first have to explain the sense in which the known solutions are approximations (see also §4.1.4).…”

Giant tachyons in the landscape

“…The D3-D5 polarization potential we are starting from depends on two parameters that cannot be fixed unless one constructs the full non-linear solution that interpolates between the infrared with anti-branes and the Klebanov-Strassler ultraviolet (this has been performed only at linearized level in [5]). However, in the final potential that we obtain the dependence on these two parameters drops out.…”

“…Second, an unstable brane can give rise to a supergravity solution that correctly captures the energy and expectation values of the corresponding unstable vacuum. This explains why the various calculations done using the perturbative anti-D3 brane solutions [5,[17][18][19][20] yielded (rather non-trivially) the energy and VEVs one would expect from a solution with antibranes. Third, the presence of a tachyon does not eliminate brane polarization -on the contrary, it makes it more likely along the tachyonic direction.…”

“…Since we do not know the non-linear solution corresponding to smeared backreacting anti-D3 branes that interpolates between the IR and the UV (this is only known at linear level [5]) our strategy is to use the most general solution sourced by anti-D3 branes compatible with the SU(2) × SU(2) symmetries of the Klebanov-Strassler background [7]. This solution is parameterized by two parameters b f and b k and we will relate them to the three parameters, m, m and µ that enter in the polarization potential.…”

“…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].…”