  We numerically study QCD with a single quark flavour on the lattice probing
predictions from effective field theories that are equivalent to minimal
super-symmetric Yang-Mills theory in the large $N_c$ limit. The hadronic
spectrum including excited states is analysed using one gauge coupling and
several physical volumes and fermion masses. We use the LapH method and also
compute disconnected diagrams. Lattice simulations with an odd number of Wilson
fermions give rise to regions of configuration space with a negative fermionic
weight entailing a sign problem. We perform a detailed analysis on the spectrum
of the Wilson-Dirac operator and report on observed cases of a negative fermion
determinant in our ensembles.
