Two loop expansion of the Schrödinger functional coupling $\alpha_{SF}$ in SU(3) lattice gauge theory

The two loop coefficient of the expansion of the Schroedinger functional coupling in terms of the lattice coupling is calculated for the SU(3) Yang-Mills theory. This coefficient is required to relate lattice data to the MS-bar-coupling. As a byproduct of the calculation, the Schroedinger functional is improved to two loop order and the three loop coefficient of the beta function in the SF-scheme is derived