标题： 关键度量与覆盖数 显示英文标题

标题： Critical Metrics and Covering Number

摘要： 在量子计算和黑洞物理中，将某些形变、无穷小酉变换自然地视为 \emph{容易的} 和其他视为 \emph{硬的} 是很合理的。 这促使人们重新考察了 $\operatorname{SU}(2^N)$ 上的右不变度量。 有人猜测存在一个关键的此类度量（在相变的意义下），并提出了一种可能的形式。 在这篇短文中，我们探讨了上同调环结构对关键度量的整体几何施加的一种限制。 显示英文摘要

摘要： In both quantum computing and black hole physics, it is natural to regard some deformations, infinitesimal unitaries, as \emph{easy} and others as \emph{hard}. This has lead to a renewed examination of right-invariant metrics on $\operatorname{SU}(2^N)$. It has been hypothesized that there is a critical such metric -- in the sense of phase transitions -- and a conjectural form suggested. In this note we explore a restriction that the ring structure on cohomology places on the global geometry of a critical metric.