Exploring the Potential Energy Landscape Over a Large Parameter-Space
City University, London（伦敦城市大学）；NanKai University（南开大学）；University of Oxford（牛津大学）；Syracuse University（雪城大学）；Colorado State University（科罗拉多州立大学）；Universität Hamburg（汉堡大学）；Trinity College, University of Oxford（牛津大学三一学院）
Yang-Hui He, Dhagash Mehta, Matthew Niemerg, Markus Rummel, Alexandru Valeanu
备注：
31 pages, 13 figures. References updated and minor typos corrected
Solving large polynomial systems with coefficient parameters are ubiquitous and constitute an important class of problems. We demonstrate the computational power of two methods--a symbolic one called the Comprehensive Gröbner basis and a numerical one called the cheater's homotopy-applied to studying both potential energy landscapes and a variety of questions arising from geometry and phenomenology. Particular attention is paid to an example in flux compactification where important physical quantities such as the gravitino and moduli masses and the string coupling can be efficiently extracted.
Exploring the landscape of (anti-) de Sitter and Minkowski solutions: group manifolds, stability and scale separation
我们在arXiv：2201.04152中对某些具有4d de Sitter、Minkowski或anti-de Sitter时空的10 d超引力解进行了分类。然后，我们在以前未探索的类中找到了新的解决方案。在本文中，我们研究它们的性质，比较它们的沼泽地植被，并作出新的观察。使用新的数值工具，我们首先确定所有的李代数下的6d群流形，使我们能够讨论他们的紧性。然后我们研究了尺度分离，并证明了相关的不可行定理。最后但并非最不重要的是，我们自动化和分析所有解决方案的稳定性。这使我们提出了无质量闵可夫斯基猜想，声称系统存在一个四维无质量标量场。
