Kac-Moody symmetries and gauged supergravity

PhD thesis
Research group: 
Quantum Gravity
Teake Nutma

Symmetry. Not only makes it our world round, but it's also what makes it go round. From the perfect circular wheels on our bikes and cars that deliver an enjoyable ride, to the error-correction protocols that keep e-mails from turning into junk; it's literally all around us. It's also symmetry that dictates the laws of nature. On the small scale the symmetry group of the Standard Model controls the interactions in molecules, atoms, and nuclei. On the large scale gravity is governed by Einstein's symmetry principle of our space-time.

This thesis deals with a certain class of symmetries known as Kac-Moody algebras. In contrast to the symmetries of the Standard Model and gravity, Kac-Moody algebras are infinite. They appear in the context of M-theory, an as of yet unknown theory that might both describe the Standard Model and gravity. In this thesis we will show how Kac-Moody algebras unify all the low-energy limits of M-theory, which are known as supergravities. Moreover, the Kac-Moody algebras contain information that corresponds exactly to all the known gauge deformations of these supergravities. We will demonstrate how to obtain the field content of the various gauged supergravities from Kac-Moody algebras, and attempt to relate the equations of motion of both sides to each other.

Publication date: 
September, 2010