Towards Supergravity Duals of Chiral Symmetry Breaking in Sasaki-Einstein Cascading Quiver Theories

TL;DR

The paper constructs a first-order, supersymmetric complex-structure deformation of the Calabi–Yau cone over $Y^{p,q}$ and embeds it into a warped IIB background with $N$ D3 branes and $M$ fractional D3 branes. It provides an explicit perturbation $f(y)={1}/{(1-cy)^2}$ and demonstrates that the deformation is a pure complex-structure change preserving $SU(3)$ holonomy to leading order, with a Kähler potential ${\cal K}=r^2$ for the cone. The authors build an imaginary-self-dual $G_3$ (and corresponding $F_3,H_3$) compatible with the deformation, analyze the warp factor via $dF_5=H_3\wedge F_3$, and show the perturbation deforms the $U(1)_R$ isometry—interpreted as chiral symmetry breaking in the dual cascading quiver theories. This work lays groundwork for holographic computations of spectra and dynamical quantities in chiral-symmetry-broken phases, extending KS/HEK-type constructions to the $Y^{p,q}$ family.

Abstract

We construct a first order deformation of the complex structure of the cone over Sasaki-Einstein spaces Y^{p,q} and check supersymmetry explicitly. This space is a central element in the holographic dual of chiral symmetry breaking for a large class of cascading quiver theories. We discuss a solution describing a stack of N D3 branes and M fractional D3 branes at the tip of the deformed spaces.