On metastable vacua and the warped deformed conifold: analytic results

Abstract

Continuing the programme of constructing the backreacted solution corresponding to smeared anti-D3 branes in the warped deformed conifold, we solve analytically the equations governing the space of first-order deformations around this solution. We express the results in terms of at most three nested integrals. These are the simplest expressions for the space of SU (2)×SU (2)×Z 2 -invariant deformations, in which the putative solution for smeared anti-D3 branes must live. We also explain why one cannot claim to identify this solution without fully relating the coefficients of the infrared and ultraviolet expansions of the deformation modes. The analytic solution we find is the first step in this direction.

Inflation and String Theory

“…The linearized solution describing p anti-D3-branes smeared around the tip of a Klebanov-Strassler throat has been obtained in [427,429,430], and passes multiple consistency checks [428,439]. The three-form flux in this solution is singular near the source [427].…”

“…The singularity is not an artifact of linearization [435], but it is not known whether the smearing approximation is responsible for the singularity. We have argued that singularities in flux should in fact be expected in this setting, but to show definitively that the singularities found in the solutions of [427,429,430] are (or are not) physical, the most compelling course is to exhibit the corresponding non-singular solution (or show that none exists).…”

“…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).…”

“…Linearization.-The linearized supergravity solution for p anti-D3-branes smeared around the S 3 has been obtained in [429,430] (for related earlier work see [442,443]), and passes non-trivial consistency checks [428,439]. The characteristic radius of curvature near the source is R p = (4πg s p) 1/4 α 1/2 , so the linearized solution can be trusted at radial distances r R p away from the tip: nearer to the tip it is inconsistent to neglect α corrections, and some of the background fields become singular.…”

“…Of course, the divergence in the energy of the electric field is removed in the quantum theory. The question, then, is whether the singularities seen in [427,429,430] are expected, and therefore plausibly resolved in the exact solution. A central concern raised by [427] is that the singularities in three-form flux "do not appear to have a distinct physical origin" [427].…”