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

点击翻译按钮获取中文摘要

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