Exceptional Holography

该奖项资助犹他州立大学奥斯卡·瓦雷拉教授的研究活动。广义相对论和量子场论历来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，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。但有没有可能这两种看似不同的理论实际上是同一枚硬币的两面呢？它们是否可以被视为一套总体物理原理的“双重”表现？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，因为它们将是等效的，尽管适用范围不同。作为他的研究项目的一部分，Varela教授将发展这一思想的各个方面，通常被称为反散射/共形场理论（AdS/CFT）对应。这项研究通过推动科学向一个基本方向发展，通过在更深层次上发展物理定律之间的关系，来推进国家利益。这个研究项目还将产生更广泛的影响，为初级物理学家提供培训，并将结果传播给整个物理界和公众。在技术上，新的超重力工具将被引入和开发，以构建弦理论背景和研究它们的全息。将分析低维的超引力理论，并构建这些模型的反德西特解。此外，基于超重力及其异常场论扩展的新技术将被开发出来，以跟踪那些低维解一直到十维和十一维，从而获得新的完整的弦理论解。同时，利用新的异常场论方法计算相应的场论算符谱和超重力有效作用。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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 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, while the latter describes the fundamental interactions --- electromagnetic, weak, and strong --- that operate at a subatomic level. But 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 albeit with different applicability regimes. As part of his research project, Professor Varela will develop aspects of this idea, generally known as the anti-deSitter/conformal field theory (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. This research project will also have broader impacts by providing training for junior physicists and by disseminating results both to the physics community at large and to the general public. More technically, new supergravity tools will be introduced and developed to construct string theory backgrounds and study their holography. Supergravity theories in lower dimensions will be analyzed and anti-de Sitter solutions to those models constructed. Further, new techniques based on supergravity and its Exceptional Field Theory extensions will be developed to track those lower-dimensional solutions all the way up to ten and eleven dimensions, thereby obtaining new fully-fledged string theory solutions. Also, the corresponding field theory operator spectra and supergravity effective actions will be computed using novel Exceptional Field Theory methods.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.