New Techniques for Holography from Supergravity

该奖项资助了犹他州立大学的奥斯卡·瓦雷拉教授的研究活动。广义相对论(理解引力的理论语言)和量子场论(理解自然基本粒子的理论语言)传统上被认为是不可调和的理论。前者支配着宇宙的大尺度结构，而后者描述了在亚原子水平上运行的基本相互作用-电磁、弱和强。更重要的是，只有后者符合量子力学的概率预期。然而，有没有可能这两种看似不同的理论实际上是一枚硬币的两面呢？它们可以被视为一套最重要的物理原理的双重表现吗？如果是这样的话，广义相对论和量子场论将是互补的，而不是相互冲突的，因为它们将是等价的，只是它们的适用范围不同。在他的研究中，Varela教授将在被称为“ADS/CFT对应”的对等框架内进一步发展这一想法。因此，这项研究通过促进科学在根本方向上的发展，通过在更深层次上发展物理定律之间的关系来促进国家利益。这项研究还将通过为初级物理学家提供培训而产生更广泛的影响。这项研究的结果也将向公众传播，重点是接触到人数不足的群体的成员。更严格地说，将研究ADS/CFT通信的各个方面，重点是在超重力条件下实现对通信的更严格控制。将引入和开发新的工具来构造包含反德西特空间的超重力方程的解。这些方法将利用高维超引力的重构，使特殊的对称性变得明显，并将提供新的有效工具来计算双场理论中的可观性。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This award funds the research activities of Professor Oscar Varela at Utah State University.General relativity (the theoretical language for understanding gravity) and quantum field theory (the theoretical language for understanding the elementary particles of nature) have traditionally been thought to be irreconcilable theories. The former governs the large-scale structure of the universe, while the latter describes the fundamental interactions —-- electromagnetic, weak, and strong —-- that operate at a subatomic level. More importantly, only the latter is consistent with the probabilistic expectations of quantum mechanics. However, is it possible that these two seemingly different theories are actually two different sides of the same coin? Could they be regarded as dual manifestations of an overarching set of physical principles? If this were the case, general relativity and quantum field theory would complement rather than conflict with each other, as they would be equivalent, differing only in their regimes of applicability. In his research, Professor Varela will further develop this idea within the framework of an equivalence called "the AdS/CFT correspondence". As such, this research advances the national interest by promoting the development of science in a fundamental direction, by developing relations among the laws of physics at deeper and deeper levels. This research will also have broader impacts by providing training for junior physicists. The results of this research will also be disseminated to the general public, with an emphasis on reaching members of under-represented groups.More technically, aspects of the AdS/CFT correspondence will be studied, with a focus in the supergravity regime where tighter control of the correspondence is attained. New tools will be introduced and developed to construct solutions to the supergravity equations that contain anti-de Sitter space. These methods will exploit the reformulations of higher-dimensional supergravities that make exceptional symmetries manifest, and will provide new efficient tools to compute observables in the dual field theories.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.