On Metastable Vacua and the Warped Deformed Conifold: Analytic Results

TL;DR

This paper analytically characterizes the space of first-order deformations around a warped deformed conifold solution with smeared anti-D3 branes, providing simplified integral expressions and insights into the solution's structure.

Contribution

It presents the first analytic solution for the space of deformations around the warped deformed conifold with smeared anti-D3 branes, expressed via nested integrals.

Findings

Derived explicit integral expressions for deformation modes.

Clarified limitations in identifying the full solution without IR and UV coefficient relations.

Provided foundational steps for future complete solutions.

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.