Matrix quantum mechanics and emergent spacetime

全息二象性是在弦理论的背景下构造的。全息意味着这些对偶性将量子力学系统与一个或多个额外维度的量子引力理论联系起来。因为这些理论来自弦理论，它们的构建依赖于自然界中未见的额外对称性的存在，比如超对称性。当我们减少超对称的数量时，精确的对偶性就不再是已知的了。在这个项目中，学生将研究具有较少超对称性的矩阵模型是否适合用于引力系统的对偶。这将通过研究这些系统的基态、它们的纠缠特性、它们的自由能和它们的非交换背景，在数值和分析上完成。这项研究的潜在应用将推动对全息对偶性的理解超越弦理论结构，这可能为我们未来的量子模拟提供可处理的量子引力模型。

Holographic dualities have been constructed in the context of string theory. Holographic means that these dualities relate quantum mechanical systems with theories of quantum gravity in one or more extra dimension. Because these theories come from string theory, their construction relies on the existence of extra symmetries not seen in nature, such as supersymmetry. When we reduce the amount of supersymmetry, exact dualities are no longer known. In this project, the student will study whether matrix models with less supersymmetry are suitable candidates for duals of gravitating systems. This will be done both numerically and analytically by studying the ground states of these systems, their entanglement properties, their free energies, and their non-commutative backgrounds. The potential applications of this research will be to push the understanding of holographic dualities beyond string theoretic constructions, which may provide us with tractable models of quantum gravity for future quantum simulations.