We highlight what seems to be a remaining subtlety in the argument for the cancellation of
the total anomaly associated with the M5-brane in M-theory. Then, we prove that this subtlety …

The heat flow for Dirac-harmonic maps on Riemannian spin manifolds is a modification of
the classical heat flow for harmonic maps by coupling it to a spinor. It was introduced by …

Not only the Dirac operator, but also the spinor bundle of a pseudo-Riemannian manifold
depends on the underlying metric. This leads to technical difficulties in the study of problems …

Let M be a smooth manifold and let g, g be Riemannian metrics on M. The metric g is said to
be conformal to g if there exists a smooth positive function u∈ C∞+(M) such that g= ug. This …

In this article, we prove that on any compact spin manifold of dimension m ≡ 0, 6, 7\mod 8
m≡ 0, 6, 7 mod 8, there exists a metric, for which the associated Dirac operator has at least …

The main result of Chapter 1 is short time existence of the heat flow for Dirac-harmonic maps
on closed manifolds. Dirac-harmonic maps are the critical points of a functional motivated by …