Conformal anomaly in the gravitationally coupled magnetic monopole and vacua effects under external conditions

在不同的外界条件下，我们将量子场论的技术应用于不同的物理系统。我们的第一个系统由与引力共形耦合的Georgi-Glasow模型(由三个标量场和SO(3)非阿贝尔规范场组成)组成。我们已经在以前的工作中证明了这个系统存在渐近反de-Sitter(ADS)时空中的磁单极子解。在这个方案中，我们通过在导致共形反常的作用中加入量子物质修正来打破共形对称性。我们的初步分析表明，爱因斯坦-希尔伯特项(广义相对论)、宇宙常数和大质量标量在原始作用中没有出现，它是在关于非平凡真空的作用展开后出现的，并主导着低能或远距离区域。共形反常确定了标度，我们预计引力常数G、宇宙常数和标量的质量可以用理论参数来表示。

We apply the techniques of quantum field theory to different physical systems under various external conditions. Our first system consists of a Georgi-Glashow model (composed of a triplet of scalar fields and SO(3) non-Abelian gauge fields) conformally coupled to gravity. We have already shown in a previous work that magnetic monopole solutions in asymptotically Anti-de Sitter (AdS) spacetime exist in this system. In this proposal we break the conformal symmetry by adding quantum matter corrections to the action leading to the conformal anomaly. Our preliminary analysis shows that an Einstein-Hilbert term (General Relativity), a cosmological constant and massive scalars, which do not appear in the original action, emerge after an expansion of the action about the non-trivial vacuum and dominate the low energy or long distance regime. The conformal anomaly fixes the scale and we anticipate that the gravitational constant G, the cosmological constant and the mass of the scalars can be expressed in terms of the parameters of the theory.