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

TL;DR

This paper constructs a supergravity dual for a metastable vacuum in the Klebanov-Strassler theory created by anti-D3-branes, analyzing the linear perturbations and matching the ADM mass with probe calculations.

Contribution

It provides a detailed supergravity description of the metastable state and identifies the lowest KK mode, including VEVs of invariant operators, extending the understanding of such vacua.

Findings

The background is regular for large p with g_s p >> 1.

The lowest KK mode of the perturbation was identified.

The ADM mass matches the probe approximation results.

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.