Higher Spin Theories, Kaluza-Klein Superspace and Higher Derivatives

该奖项资助了德克萨斯A&M大学的凯特琳·贝克尔教授和埃尔金·塞兹金教授的研究活动。为了在基本层面上描述自然，物理学家使用了两种不同的理论和一套非常不同的规则：量子理论和广义相对论。量子理论被用来描述非常小距离的自然(原子和基本粒子的世界)。相比之下，广义相对论被用来描述非常大距离的自然(行星、恒星和星系的领域)。找到一套在所有距离都有效的一致和统一的规则，同时描述所有基本的相互作用，这一任务长期以来一直是物理学中的一个巨大挑战。实现这一目标的最有希望的候选者被称为“弦理论”，因为它基于这样的前提，即所有基本粒子对应于一个令人难以置信的小基本弦的不同振动模式。在描述低能现象时，弦理论产生了爱因斯坦引力理论的一个版本，被称为“超引力”。然而，随着我们探测更短的距离(或相当于更高的能量)，弦理论预测了超重力的偏离。弦理论的一个重要挑战是计算和理解这些偏差。作为他们研究的一部分，贝克尔和塞兹金教授将致力于解决这个问题的一些研究方向，其中许多对早期宇宙的描述有着深远的影响。该项目还有望通过加强弦理论和数学之间的众多接口而产生更广泛的影响，并通过促进科学进步和寻找描述我们宇宙未知运作的新物理定律来促进国家利益。PIS还将为博士后和学生提供批判性培训，并计划就他们的研究成果进行公开讲座。更技术上，Becker和Sezgin教授的目标是构建不同超弦理论和M理论紧凑化的完整时空有效作用，以显示明显的脱离壳层超对称的形式，目标是找到斜率参数中的所有阶。对于更高维的超引力理论，没有(有限的)脱离壳层的公式。因此，编写高阶导数的超对称作用量变得非常困难。贝克尔和塞兹金教授计划在4D，N=1超空间中重新表述更高维的超重力理论，特别是11D超重力，这是允许(有限)脱离壳层公式的最简单的超空间之一。当然，在四个时空维度中选择明显的超对称性是出于现象学的动机，贝克尔和塞兹金教授设想了他们的工作在现象学上的大量应用。他们还将探索物质耦合、隐藏的对称性、反常和更高自旋理论的精确解。他们还将构建物质耦合超重力的高阶导数耦合，调查其真空，研究其对偶对称性及其嵌入弦理论。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 Professors Katrin Becker and Ergin Sezgin at Texas A&M University.To describe nature at the fundamental level, physicists use two different theories with very different set of rules: quantum theory and general relativity. Quantum theory is used to describe nature at very small distances (the world of atoms and elementary particles). By contrast, general relativity is used to describe nature at very large distances (the realm of planets, stars and galaxies). The task of finding a consistent and unified set of rules that are valid at all distances, and at the same time describing all fundamental interactions, has long been a great challenge in physics. The most promising candidate to achieve this goal is called "string theory" since it is based on the premise that all elementary particles correspond to different vibrational modes of an incredibly small fundamental string. In describing phenomena at low energies, string theory produces a version of Einstein's theory of gravity known as "supergravity". However, as we probe shorter distances (or equivalently higher energies), string theory predicts deviations from supergravity. One of the important challenges in string theory is to compute and understand these deviations. As part of their research, Professors Becker and Sezgin will pursue a number of research directions that deal with this problem, many of which have profound consequences for the description of the early universe. This project is also envisioned to have broader impact by strengthening the numerous interfaces between string theory and mathematics, and advances the national interest by promoting progress in science and seeking new physical laws that describe the uncharted workings of our universe. The PIs will also provide critical training to postdocs and students, and plan to give public lectures on their research results.More technically, Professors Becker and Sezgin aim to construct the full space-time effective action of different superstring- and M-theory compactifications in a form displaying manifest off-shell supersymmetry with the goal of finding all orders in the slope parameter. For higher-dimensional supergravity theories there is no (finite) off-shell formulation. As a result, writing higher derivative supersymmetric actions turns out to be very difficult. Professors Becker and Sezgin plan to reformulate higher-dimensional supergravity theories, in particular 11D supergravity, in 4D, N = 1 superspace which is one of the simplest superspaces allowing (finite) off-shell formulations. Choosing manifest supersymmetry in four space-time dimensions is, of course, motivated by phenomenology, and Professors Becker and Sezgin envision a host of phenomenological applications of their work. They will also explore matter couplings, hidden symmetries, anomalies, and exact solutions of higher spin theories. They will also construct the higher derivative couplings of matter-coupled supergravity, investigate its vacua, and study its duality symmetries and its embedding into string theory.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.