The thesis covers two topics in string theory and quantum field theory. First, we realize metastable vacua in various supersymmetric gauge theories. Specifically, we consider the Coulomb branch of any N = 2 supersymmetric gauge theory, and perturb it by a superpotential and engineer a metastable vacuum at a point. We also study its relation to Kahler normal coordinates and Fayet-Iliopoulos terms. Having studied the metastable construction, we apply this to general gauge mediation. We show how to compute the current correlators when the hidden sector is strongly coupled in specific examples.ududNext, we consider gauge/gravity dualities. We apply dualities to the investigation of various strongly coupled field theories. In one example, we construct M-theory supergravity solutions with the nonrelativistic Schroedinger symmetry starting from the warped AdS_5 metric with N = 1 supersymmetry. We impose that the lightlike direction is compact by making it a nontrivial U(1) bundle over the compact space. In another example, we show that, in a gravity theory with a Chern-Simons coupling, the Reissner-Nordstrom black hole in anti-de Sitter space is unstable depending on the value of the Chern-Simons coupling. The analysis suggests that the final configuration is likely to be a spatially modulated phase.
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机译：本文涵盖了弦论和量子场论两个主题。首先，我们在各种超对称规范理论中实现了亚稳态真空。具体来说，我们考虑任何N = 2超对称规范理论的库仑分支，并通过超电势对其进行扰动并在一个点上设计亚稳态真空。我们还研究了它与Kahler法向坐标和Fayet-Iliopoulos项的关系。研究了亚稳构造后，我们将其应用于一般规范的调解。在特定示例中，我们显示了当隐藏扇区强烈耦合时如何计算当前相关器。 ud ud接下来，我们考虑轨距/重力对偶。我们将对偶应用于各种强耦合领域理论的研究。在一个示例中，我们从N = 1的超对称扭曲AdS_5度量开始，以非相对论的薛定inger对称性构造M理论超重力解。我们通过在紧凑空间上使其成为非平凡的U（1）束，来强加光似方向的紧凑性。在另一个示例中，我们表明，在具有Chern-Simons耦合的重力理论中，取决于Chern-Simons耦合的值，anti-de Sitter空间中的Reissner-Nordstrom黑洞是不稳定的。分析表明，最终配置可能是空间调制的相位。
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