论文标题
引导矩阵量子力学
Bootstrapping Matrix Quantum Mechanics
论文作者
论文摘要
大型$ n $矩阵量子力学对于全息二元性是至关重要的，但在最有趣的情况下却无法解决。我们表明，这些理论中的频谱和简单的期望值可以通过“ bootstrap”方法数量获得。在这种方法中，操作员的期望值与对称性相关 - 例如时间翻译和$ su（n）$量规的不变性 - 然后受到某些阳性约束的限制。我们首先演示了该方法如何有效地解决常规量子振荡振荡器。然后，我们重现了已知的$ N $单基质量子力学的已知解决方案。最后，我们以大于$ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n的量子力学的基础状态提出了新的结果。
Large $N$ matrix quantum mechanics is central to holographic duality but not solvable in the most interesting cases. We show that the spectrum and simple expectation values in these theories can be obtained numerically via a `bootstrap' methodology. In this approach, operator expectation values are related by symmetries -- such as time translation and $SU(N)$ gauge invariance -- and then bounded with certain positivity constraints. We first demonstrate how this method efficiently solves the conventional quantum anharmonic oscillator. We then reproduce the known solution of large $N$ single matrix quantum mechanics. Finally, we present new results on the ground state of large $N$ two matrix quantum mechanics.
