On gravity dual of a metastable vacuum in Klebanov-Strassler theory

TL;DR

This work presents a controlled gravity dual for the metastable vacuum induced by a stack of anti-D3 branes at the Klebanov-Strassler tip in the regime $g_s p \gg 1$, using a linearized perturbation around KS in the SU(2)×SU(2) sector. By imposing consistent IR and UV boundary conditions, the authors extract the lowest KK mode, showing nonzero VEVs for invariant operators at order $p$ and validating the construction through an ADM mass that matches the probe calculation. They also derive a gravity dual for KS perturbed in the UV by small $W^2$ and $W^2\bar{W}^2$ operators, and illustrate a specific softly broken SUSY deformation by gaugino masses. Together, these results provide a robust, semi-analytic framework for metastable SUSY breaking in KS and for exploring softly broken SUSY deformations via holography.

Abstract

We discuss a supergravity description of the metastable state that is created by a stack of anti-D3-branes placed at the tip of the KS background. When the number p of the anti-D3-branes is large g_s p >> 1 the characteristic curvature of the corresponding gravity dual is large in stringy units and one may expect the background to be regular everywhere. Starting from the distances of order R ~ (g_s p)^{1/4} away from the tip the new background can be well approximated by a linear perturbation around KS. By applying the appropriate boundary conditions in both IR and UV we found the lowest KK mode of the corresponding linear perturbation. The solution we found contains VEVs of the SU(2)x SU(2) invariant operators at the linear order in p. As a non-trivial check we calculate the ADM mass which exactly matches the probe approximation. As a byproduct we also found a gravity background dual to the KS theory deformed by the operators W^2 and W^2\bar{W}^2 with small coefficients.