标题： 关于模糊球上共形生成元的显式构造的注记 显示英文标题

标题： Note on explicit construction of conformal generators on the fuzzy sphere

摘要： 球面上的最低朗道能级最近被提出作为三维共形场论的连续正则化方法，即所谓的模糊球正则化。 在这篇短文中，我们提出了用显微镜下哈密顿量来构造模糊球上的共形生成元的明确方法。 具体来说，我们构造了平移生成元和特殊共形变换生成元，这些生成元用于定义共形主态，因此特别值得关注。 我们将这种方法应用于一个具体的例子——用模糊球正则化的三维伊辛共形场论。 我们证明它可以帮助捕获自旋为$\ell < 4$且标度维数为$\Delta < 7$的所有主态。 特别是，我们的方法可以清楚地将主态与其他尺度维数相差$1\%$的态分开，而仅依靠与主态相关的共形塔很难做到这一点。 显示英文摘要

摘要： The lowest Landau level on the sphere was recently proposed as a continuum regularization of the three-dimensional conformal field theories, the so-called fuzzy sphere regularization. In this note, we propose an explicit construction of the conformal generators on the fuzzy sphere in terms of the microscopic Hamiltonian. Specifically, we construct the generators for the translation and special conformal transformation, which are used in defining the conformal primary states and thus are of special interest. We apply our method to a concrete example, the fuzzy sphere regularized three-dimensional Ising conformal field theory. We show that it can help capture all primaries with spin $\ell < 4$ and scaling dimension $\Delta < 7$. In particular, our method can clearly separate the primary from other states that differ in scaling dimension by $1\%$, making it hard otherwise based solely on using the conformal tower associated with the primaries.