Explicit Analysis of Kahler Deformations in 4D N=1 Supersymmetric Quiver Theories

TL;DR

This paper constructs a new class of $ =1$ quiver gauge theories from $ =2$ theories on wrapped D5 branes, explicitly analyzing Kahler deformations via CY3 geometry and establishing superfield correspondences with complex deformation models.

Contribution

It introduces a novel method to realize $ =1$ quiver gauge theories through Kahler deformations, linking geometric deformations to gauge theory dynamics.

Findings

Kahler deformations correspond to the real part of the integral of the (2,1) form of CY3.

The constructed models show spontaneous breaking of the gauge group to SU(N).

Superfield correspondence with complex deformation models is established.

Abstract

Starting from the $\mathcal{N}=2$ SYM$_{4}$ quiver theory living on wrapped $% N_{i}D5$ branes around $S_{i}^{2}$ spheres of deformed ADE fibered Calabi-Yau threefolds (CY3) and considering deformations using \textit{% massive} vector multiplets, we explicitly build a new class of $\mathcal{N}% =1 $ quiver gauge theories. In these models, the quiver gauge group $% \prod_{i}U(N_{i}) $ is spontaneously broken down to $% \prod_{i}SU(N_{i}) $ and Kahler deformations are shown to be given by the real part of the integral $(2,1) $ form of CY3. We also give the superfield correspondence between the $\mathcal{N}=1$ quiver gauge models derived here and those constructed in hep-th/0108120 using complex deformations. Others aspects of these two dual $\mathcal{N}=1$ supersymmetric field theories are discussed.