Gradings on walled Brauer algebras and Khovanov's arc algebra

We introduce some Z-graded versions of the walled Brauer algebra Br,s(δ), working over a field of characteristic zero. This allows us to prove that Br,s(δ) is Morita equivalent to an idempotent truncation of a certain infinite dimensional version of Khovanov's arc algebra. We deduce that the walled Brauer algebra is Koszul whenever δ≠0.