Supergravity Tools for Holography

该奖项资助了犹他州州立大学的奥斯卡·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。 前者支配着宇宙的大尺度结构，显然是经典的。 后者描述了基本的相互作用-电磁的，弱的，强的-在亚原子水平上运行。 但是，有没有可能这两个看似不同的理论实际上是同一枚硬币的两个不同面？ 它们能被看作是一套支配性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相互补充，而不是相互冲突，因为它们是等价的，尽管适用范围不同。 在他的研究中，瓦雷拉教授将发展这一想法的各个方面，这通常被称为所谓的“AdS/CFT对应”。 这项研究通过促进科学在根本方向上的发展，通过在越来越深的层次上发展物理定律之间的关系，促进了国家利益。 它还将通过为初级物理学家提供培训并向公众传播其结果，特别是向代表性不足的群体的成员传播其结果，从而产生更广泛的影响。更技术性地，瓦雷拉教授将研究AdS/CFT对应的不同方面，重点关注超重力领域，其中实现了更严格的对应控制。 将引入和开发新的工具，以构建包含反德西特空间的超重力方程的解。 这些方法将利用更高维的超引力的重新表述，使特殊的对称性表现出来，也将利用限制张量和对偶层次。 有效的低维超引力理论与AdS真空将被构建和他们的嵌入弦理论阐明。 最后，我们将研究这些新的弦理论解的场论性质。

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.