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

这项由肯塔基大学四位物理学家提出的建议涉及高能物理、数学物理和凝聚态物理之间的最新理论发展。在过去的十年里，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”，即标准微扰数学处理无效的理论。这一工具是理论高能物理发展的结果，已经被用于研究高能物理和核物理交界处的系统，例如夸克-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。这项建议旨在开发利用ADS/CFT通信的技术，以解决平衡和非平衡多体系统在其临界点附近或临界点处的难题。PI的目的还在于研究物质拓扑态的纠缠熵。如果成功，这将代表着一种解决凝聚态物理中极其困难的问题的全新方式，并有可能在凝聚态物理学和ADS/CFT通信本身的数学方面带来重要的新见解。因此，这一提议不仅在范围上是跨学科的，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、数学物理和凝聚态物理之间的协同作用。这项提议的其他更广泛的影响集中在培训将在这一新兴学科工作的博士后研究人员。

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.