Holography, Supersymmetry, and Numerics in Quantum Critical and Quantum Lifshitz Theories

这个来自肯塔基州大学的四位物理学家的提议涉及高能物理学、数学物理学和凝聚态物理学之间的最新理论发展。在过去的十年中，所谓的AdS/CFT对应已被证明是分析强耦合理论的一个非常有用的理论“工具”，即，标准的微扰数学处理无效的理论。 这一工具是理论高能物理学发展的产物，已被用于研究高能物理与核物理交界处的系统，如夸克-胶子等离子体。 然而，就在过去的几年里，AdS/CFT工具的一个新方向已经变得明显-这是研究凝聚态物理中的强耦合系统。该建议的目的是发展techniques使用AdS/CFT对应，以解决困难的问题，在平衡和非平衡多体系统附近或在其临界点。PI的目标还包括研究物质拓扑状态的纠缠熵。如果成功，这将代表一种全新的方式来解决凝聚态物理中极其困难的问题，并有可能在凝聚态物理和AdS/CFT对应本身的数学中产生重要的新见解。 因此，这一提议不仅在其范围内是跨学科的，而且在其研究潜力方面也具有潜在的变革性，利用了理论高能物理学，数学物理学和凝聚态物理学之间的协同作用。 这项建议的其他更广泛的影响集中在培养博士后研究人员谁将在这个新兴的学科工作。

This proposal from four physicists at the University of Kentucky concerns recent theoretical developments at the border between high-energy physics, mathematical physics, and condensed-matter physics. Over the past decade, the so-called AdS/CFT correspondence has proven to be a very useful theoretical "tool" for analyzing strongly coupled theories, i.e., theories for which a standard perturbative mathematical treatment is ineffective. This tool, which resulted from developments in theoretical high-energy physics, has already been used in order to study systems at the interface of high-energy and nuclear physics, such as the quark-gluon plasma. However, just in the past few years, a new direction for the AdS/CFT tool has become apparent --- this is to study strongly coupled systems in condensed-matter physics. This proposal aims to develop teachniques using the AdS/CFT correspondence in order to address difficult problems in equilibrium and non-equilibrium many-body systems near or at their critical points. The PI's also aim to study the entanglement entropy of topological states of matter. If successful, this would represent an entirely new way of attacking extremely difficult problems in condensed-matter physics, and has the potential to lead to important new insights in both condensed-matter physics and for the mathematics of the AdS/CFT correspondence itself. Thus, this proposal is not only interdisciplinary in its scope, but also potentially transformative in its research potential, exploiting the synergy between theoretical high-energy physics, mathematical physics, and condensed-matter physics. Additional broader impacts of this proposal are focused on the training of postdoctoral researchers who will work in this newly emerging discipline.