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

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.