Exploring Structure and Symmetry in String Theory and Field Theory

该奖项资助了芝加哥大学Savdeep Sethi教授的研究活动。 空间和时间的起源是自然界经久不衰的奥秘之一。 空间和时间是在某种大爆炸中出现的吗？ 宇宙会在一次大挤压中结束吗？ 真的有多重宇宙的可能性吗？ 为了回答这些关于空间和时间本质的基本问题，我们需要引力的量子理论。 弦理论是我们最好的候选理论。 在他的研究中，塞西教授的目标是探索弦理论和粒子物理学家和凝聚态物理学家感兴趣的所谓“量子场论”的结构和对称性。 因此，这项研究计划通过推进美国基础科学基础设施的发展符合国家利益。 这项研究计划还在三个领域产生了更广泛的影响。 首先是为本科生提供研究机会，包括继续参加芝加哥大学的少数民族和妇女暑期REU机会计划。 第二个是通过继续参与太空探索者内城K-12丰富计划和终身学习（L3）计划。 最后一个方面是通过在学校和研讨会上的讲座，通过直接合作，以及通过组织相关的科学会议，加强与宇宙学家和数学家的跨学科联系。更技术性地说，塞西教授的研究中心的目标围绕两个广泛的主题。 这项研究的“结构”方面涉及探索场论和弦论中的景观。 这将涉及一些主题，其中包括从场论的角度描述通量背景，并通过反德西特空间解的新景观在弦论中实现; M理论和IIA型弦论中通量真空的发展;反膜在通量真空中的作用;弦理论中膨胀和德西特结构的限制探索;利用弦畴壁解加速时空的构建;以及二维手征规范理论的研究及其与新几何结构的关系。 相比之下，该提议的“对称性”方面涉及探索引力和有效场论中自发破缺对称性的含义。 引力的问题围绕着对称性在多大程度上决定了引力块的动力学。 在更广泛的背景下，反常和非反常的全局对称性可以限制有效的场论耦合，并对凝聚态系统（如量子霍尔系统）产生影响。 最后一组问题以两种方式涉及超对称性：第一，开发一个符号计算包，可以生成具有高阶导数耦合的超对称拉格朗日量（这是一个长期需要的工具，在弦理论和场论中都有大量应用）;第二，探索超对称量子力学模型的真空结构中令人惊讶的简化。

This award funds the research activities of Professor Savdeep Sethi at the University of Chicago. The origins of space and time are among the enduring mysteries of nature. Did space and time emerge in some kind of Big Bang? Will the universe end in a Big Crunch? Is there really a multiverse of possibilities? In order to answer such basic questions about the nature of space and time, we need a quantum theory of gravity. String theory is our best candidate for such a theory. In his research, Professor Sethi aims to explore structure and symmetry in both string theory and the kinds of so-called "quantum field theories" of interest to particle physicists and condensed-matter physicists. This research program is therefore in the national interest by advancing the development of the infrastructure of basic science in the United States. This research program also has concomitant broader impacts in three areas. The first comes from providing research opportunities for undergraduates, including continued participation in the Summer REU Opportunities for Minorities and Women program at the University of Chicago. The second is through continued participation in both the Space Explorers inner-city K-12 enrichment program and the Life-Long Learning (L3) program. The final aspect involves improved interdisciplinary ties with both cosmologists and mathematicians through lectures at schools and workshops, through direct collaboration, and through the organization of relevant scientific meetings.More technically, the goals of Professor Sethi's research center around two broad themes. The "structure" aspect of this research involves exploring landscapes in field theory and string theory. This will involve a number of topics, among them the description of flux backgrounds from a field-theory perspective and their realization in string theory via a novel landscape of anti-de Sitter space solutions; the development of flux vacua in M-theory and type IIA string theory; the role of anti-branes in flux vacua; the exploration of constraints on inflating and de Sitter constructions in string theory; the construction of accelerating space-times using stringy domain-wall solutions; and the study of chiral gauge theory in two dimensions and its relation to new geometric structures. By contrast, the "symmetry" aspect of the proposal involves exploring the implications of spontaneously broken symmetries in gravity and in effective field theory. The questions in gravity revolve around the extent to which the dynamics of gravitational lumps is determined by symmetry. In a broader context, anomalous and non-anomalous global symmetries can constrain effective field theory couplings with implications for condensed-matter systems such as quantum Hall systems. The final set of questions involve supersymmetry in two ways: first to develop a symbolic computation package that can generate supersymmetric Lagrangians with higher-derivative couplings (a long-needed tool that will have a host of applications in both string theory and field theory), and second to explore surprising simplifications in the vacuum structure of supersymmetric quantum-mechanics models.