Supersymmetry Relics in One-Flavor QCD from a New1/NExpansion

We suggest a new large-$N_c$ limit for multiflavor QCD. Since fundamental and two-index antisymmetric representations are equivalent in SU(3), we have the option to define $\mathrm{S}\mathrm{U}(N_c)$ QCD keeping quarks in the latter. We can then define a new $1/N_c$ expansion (at a fixed number of flavors $N_f$) that shares appealing properties with the topological (fixed $N_f/N_c$) expansion while being more suitable for theoretical analysis. In particular, for $N_f=1$, our large-$N_c$ limit gives a theory that we recently proved to be equivalent, in the bosonic sector, to $\mathcal{N}=1$ supersymmetric gluodynamics. Using known properties of the latter, we derive several qualitative and semiquantitative predictions for $N_f=1$ massless QCD that can be easily tested in lattice simulations. Finally, we comment on possible applications for pure SU(3) Yang-Mills theory and real QCD.