Event

Talk
A supersymmetric approach to special metrics in dimension 8
Dr. Frederik Witt (FU Berlin)
27 Jun 2006, 15:00 – 16:00

Dimension 8 is extremely rich in special metrics, i.e. metrics associated with a G- structure for G a proper subgroup of SO(8). In this talk, I want to describe a unified approach to PSU(3)-, - (almost quaternionic Kähler) and Spin(7)-structures. The latter two appear in Berger's list of Riemannian holonomy groups and are usually defined by a closed self-dual 4-form while PSU(3) appeared in connection with Hitchin's variational principle and is defined by a closed and co-closed 3-form. In the case of Spin(7), it is well-known that this geometry can be rephrased in terms of a unit spinor which is why this group plays a predominant rôle in supersymmetric string compactifications. On the other hand, this invariant spinor also defines an isometry between vectors and chiral spinors. I will explain how one can equally characterise PSU(3)- and -structures by the existence of such an isometry, giving rise to a spin 3/2-field (also known as Rarita-Schwinger field in supergravity). Morever, the corresponding differential forms are closed and co-closed if and only if the corresponding spinorial invariant is harmonic with respect to the twisted Dirac operator. In the case of Spin(7) this is equivalent to the holonomy reducing to this group.

Related to:

• Frederik Witt