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 analyzed 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.