The underlying symmetries of string theory, notably higher-spin symmetries and Kac-Mood algebras

弦理论的基本对称性，特别是高自旋对称性和 Kac-Mood 代数

• 批准号: 95154062
• 负责人: Professor Dr. Olaf Hohm
• 金额: --
• 依托单位: Institut für Physik
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2008
• 资助国家: 德国
• 起止时间: 2007-12-31 至 2011-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/95154062?language=en
• 关键词: underlying; symmetries; string; theory; notably

String theory is one of the most promising candidates for a theory reconciling general relativity with quantum theory. Though it provides a consistent perturbative framework of quantum gravity, its present status is unsatisfactory since the underlying (symmetry-) principles of string theory (or of its modern offspring called M-theory) remain unknown. There are two basic hints where to look for these symmetries: First, the low-energy limit of string theory, namely supergravity, exhibits hidden symmetries when reduced to low dimensions. Therefore these symmetries (or possible extensions thereof, the so-called Kac-Moody algebras) will most likely play a role in the original, higher-dimensional theory — leading to a Supergravity/Kac-Moody correspondence. Second, the massive string modes beyond the regime of supergravity are of higher spin, and it is an old idea that these represent a broken phase of a theory with an underlying higher-spin gauge symmetry. Finally, in the form of the so-called ‘dual graviton’ higher-spin fields also enter the Kac-Moody approach. My aim is to further investigate the Supergravity/Kac-Moody correspondence for the regime of gauged or massive supergravity. It can be argued that these provide the first truly independent verification of the conjectured correspondence beyond the symmetries which are already known to appear upon dimensional reduction. Moreover, I plan to extend my research on Chern-Simons theories based on higher-spin algebras, which may provide valuable insights into string or M-theory.Keywords: supergravity, hidden symmetries, Kac-Moody algebras, dual graviton, higher-spin fields

弦理论是调和广义相对论和量子理论的最有希望的候选理论之一。尽管它提供了一个一致的量子引力微扰框架，但它的现状并不令人满意，因为弦理论(或其现代后代M理论)的基本(对称)原理仍然未知。在哪里寻找这些对称性有两个基本提示：第一，弦理论的低能量极限，即超重力，当缩减到低维时，会显示出隐藏的对称性。因此，这些对称性(或其可能的扩展，即所谓的Kac-Moody代数)很可能会在原始的、更高维度的理论中发挥作用--导致超重力/Kac-Moody对应。其次，超出超引力范围的大质量弦模式具有更高的自旋，这是一个古老的想法，即这些模式代表着一个具有更高自旋规范对称性的理论的破缺阶段。最后，以所谓的“双引力子”的形式，更高自旋场也进入了卡克-穆迪方法。我的目标是进一步研究超重力/卡克-穆迪对应的测量超重力或大质量超重力。可以争辩说，除了已知的降维时出现的对称性之外，这些方法首次真正独立地验证了猜想的对应性。此外，我计划扩展我对基于高自旋代数的Chern-Simons理论的研究，这可能会为弦理论或M-理论提供有价值的见解。关键词：超引力、隐藏对称性、Kac-Moody代数、对偶引力子、高自旋场