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

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。尽管它为量子引力提供了一个一致的微扰框架，但它目前的状态并不令人满意，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：首先，弦理论的低能量极限，即超引力，在降维到低维时表现出隐藏的对称性。因此，这些对称性（或其可能的延伸，即所谓的Kac-Moody代数）很可能在原始的高维理论中发挥作用——导致超引力/Kac-Moody对应。其次，超引力之外的大质量弦模式具有更高的自旋，这是一个古老的观点，认为这些模式代表了一个具有潜在更高自旋规范对称的理论的破碎阶段。最后，以所谓的“双引力子”的形式，高自旋场也进入了Kac-Moody方法。我的目标是进一步研究超重力/Kac-Moody对应的测量或大质量超重力。可以说，这些理论提供了第一次真正独立的验证，证明了在已知的降维过程中出现的对称性之外的推测的对应性。此外，我计划扩展我对基于高自旋代数的chen - simons理论的研究，这可能为弦或m理论提供有价值的见解。关键词：超重力，隐藏对称，Kac-Moody代数，对偶引力子，高自旋场

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