Gravity duals for a class of UV complete minimally supersymmetric nonconformal gauge theories require deformed conifolds with fluxes. However these manifolds do not allow for the standard Kähler or conformally Kähler metrics on them, instead the metrics are fully non-Kähler. We take a generic such configuration of a non-Kähler deformed conifold with fluxes and ask what constraints do supersymmetry impose in the baryonic branch. We study the supersymmetry conditions and show that for the correct choices of the vielbeins and the complex structure all the equations may be consistently solved. The constraints now lead not only to the known cases in the literature but also to some new backgrounds. We also show how geometric features of these backgrounds, including the overall warp-factor and the resolution parameters, can be seen on the field theory side from perturbative “probe-brane” type calculations by Higgsing the theory and studying one-loop 4-point functions of vector and chiral multiplets. Finally we discuss how UV completions of these gauge theories may be seen from our setup, both from type IIB as well as from the T-dual type IIA brane constructions.

中文翻译：

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重子分支中的非 Kähler 变形锥体、紫外完成和超对称约束

一类紫外完全最小超对称非共形规范理论的重力对偶需要具有通量的变形锥体。然而，这些流形不允许在其上使用标准的 Kähler 或保形 Kähler 度量，相反，这些度量是完全非 Kähler 的。我们采用具有通量的非 Kähler 变形 conifold 的通用配置，并询问超对称性在重子分支中施加了哪些约束。我们研究了超对称性条件，并表明对于正确选择vielbeins和复杂结构，所有方程都可以一致地求解。现在，这些限制不仅导致了文献中的已知案例，而且还导致了一些新的背景。我们还展示了这些背景的几何特征，包括整体扭曲因子和分辨率参数，通过希格斯理论和研究向量和手性多重态的单环 4 点函数，可以在场论方面从微扰“探针膜”类型计算中看到。最后，我们讨论了如何从我们的设置中看到这些规范理论的 UV 完成，包括 IIB 型和 T-dual IIA 型膜结构。