On Metastable Vacua and the Warped Deformed Conifold: Analytic Results

TL;DR

The paper delivers a compact analytic construction of the space of first-order, SU(2)×SU(2)×Z2-invariant deformations around the Klebanov–Strassler background, aimed at describing smeared anti-D3 branes in the warped deformed conifold. By employing the Borokhov–Gubser method together with the Papadopoulos–Tseytlin ansatz, the authors reduce the eight conjugate-momentum equations to expressions in terms of two fundamental integrals, and express seven of the deformation modes with at most double integrals (the warp-factor related mode via three nested integrals). The results provide explicit, largely analytic formulas for the deformation fields, enabling the subsequent matching of infrared and ultraviolet expansion data and the extraction of the anti-D3 charge to force ratio via a numerical integration. This analytic framework significantly streamlines the path toward testing whether the backreacted anti-D3 solution describes a metastable vacuum and clarifies the role of IR singularities in the backreaction problem.

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 $SU(2) \times SU(2) \times \ZZ_2$-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.