We study scalar fields propagating on Euclidean dynamical triangulations (EDTs). In this work, we study the interaction of two scalar particles, and we show that in the appropriate limit we recover an interaction compatible with Newton’s gravitational potential in four dimensions. Working in the quenched approximation, we calculate the binding energy of a two-particle bound state, and we study its dependence on the constituent particle mass in the nonrelativistic limit. We find a binding energy compatible with what one expects for the ground state energy by solving the Schrödinger equation for Newton’s potential. Agreement with this expectation is obtained in the infinite-volume, continuum limit of the lattice calculation, providing nontrivial evidence that EDT is in fact a theory of gravity in four dimensions. Furthermore, this result allows us to determine the lattice spacing within an EDT calculation for the first time, and we find that the various lattice spacings are smaller than the Planck length, suggesting that we can achieve a separation of scales and that there is no obstacle to taking a continuum limit. This lends further support to the asymptotic safety scenario for gravity.

中文翻译：

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来自晶格量子引力的牛顿束缚

我们研究在欧几里得动态三角剖分 (EDT) 上传播的标量场。在这项工作中，我们研究了两个标量粒子的相互作用，并表明在适当的极限下，我们恢复了与牛顿在四个维度上的引力势兼容的相互作用。在淬火近似中，我们计算了两粒子束缚态的结合能，并研究了它对非相对论极限中组成粒子质量的依赖性。通过求解牛顿势的薛定谔方程，我们找到了一种与人们对基态能量预期相符的结合能。在晶格计算的无限体积连续极限中获得了与此期望的一致，这提供了证明 EDT 实际上是四维引力理论的重要证据。此外，这个结果让我们第一次在 EDT 计算中确定了晶格间距，我们发现各种晶格间距都小于普朗克长度，表明我们可以实现尺度的分离，并且没有障碍取连续极限。这进一步支持重力的渐近安全场景。