Supergravity Tools for Holography

该奖项资助犹他州立大学的奥斯卡·瓦雷拉教授的研究活动。广义相对论和量子场论传统上被认为是不可调和的理论。前者主宰着宇宙的大尺度结构，显然是古典的。后者描述了在亚原子水平上运行的基本相互作用--电磁的、弱的和强的。但是，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相互补充而不是冲突的，因为它们将是等价的，尽管适用范围不同。在他的研究中，Varela教授将发展这一想法的各个方面，这就是通常所说的“ADS/CFT对应”。这项研究通过推动科学向根本方向发展，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。它还将产生更广泛的影响，为初级物理学家提供培训，并将其结果传播给公众，特别是代表人数不足的群体的成员。更严格地说，Varela教授将研究ADS/CFT通信的不同方面，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，并将利用限制张量和对偶层次。我们将构建有效的具有ADS真空的低维超引力理论，并阐明它们在弦理论中的嵌入。最后，我们将研究这些新的弦理论解的场论对偶。

This award funds the research activities of Professor Oscar Varela at Utah State University.General relativity and quantum field theory have traditionally been thought to be irreconcilable theories. The former governs the large-scale structure of the universe and is manifestly classical. The latter describes the fundamental interactions --- electromagnetic, weak, and strong --- that operate at a subatomic level. But, could it be possible that these two seemingly different theories were 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 each other, as they would be equivalent, albeit with different applicability regimes. In his research, Professor Varela will develop aspects of this idea, which is commonly known as the so-called "AdS/CFT correspondence". 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. It will also have broader impacts by providing training for junior physicists and by disseminating its results to the general public, especially to members of under-represented groups.More technically, Professor Varela will study different aspects of the AdS/CFT correspondence 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 also utilize restricted tensor and duality hierarchies. Effective lower-dimensional supergravity theories with AdS vacua will be constructed and their embeddings into string theory elucidated. Finally, the field theory duals of those new string theory solutions will be investigated.