The Mesonic Branch of the Deformed Conifold

TL;DR

The paper constructs a gravity dual for the mesonic branch of the KS deformed conifold by placing a stack of D3-branes at the North pole of the non-vanishing $S^3$ and solving the 6d Laplace equation for the warp factor in a coordinate system that reveals the $S^2$–$S^3$ split. The warp factor $h=h_{KS}+H_{D3}$ develops an $AdS_5$ throat near the branes, corresponding to an RG flow toward ${\cal N}=4$ $SU(N)$ SYM in the IR. Expanding the meson superpotential around the North-pole VEV reproduces the cubic ${\cal N}=4$ SYM superpotential, linking the gravity solution to the expected IR EFT. The work provides a concrete holographic realization of the mesonic branch, preserving baryonic symmetry and clarifying the emergence and limitations of Goldstone modes in this setup.

Abstract

Using coordinates that manifest the S^2-S^3 split of the base, we study D3-branes localized on the three-sphere in the Klebanov-Strassler background. We find a numerical solution for the warp factor and show the emergence of the AdS throat near the stack. In the dual gauge theory, this corresponds to an RG flow along the mesonic branch. We demonstrate how the cubic superpotential of the N=4 SYM theory emerges at the end of the RG flow.

Figures (2)

• Figure 1: A schematic picture of the (deformed) conifold. NP stands for the North Pole of the non-vanishing three sphere at the tip. Our D-branes are at NP.
• Figure 2: Plots of $\alpha H_l(\tau)$ where $\frac{1}{\alpha}=\frac{ 2^{2/3}}{\pi^2\epsilon^{8/3}} C$, for $l=0, 1, 3$. The curve rises as $l$ increases.