Chiral spin liquids in triangular lattice SU(N) fermionic Mott insulators with artificial gauge fields

We show that, in the presence of a $\pi \mathrm{/}2$ artificial gauge field per plaquette, Mott insulating phases of ultra-cold fermions with $SU(N)$ symmetry and one particle per site generically possess an extended chiral phase with intrinsic topological order characterized by a multiplet of $N$ low-lying singlet excitations for periodic boundary conditions, and by chiral edge states described by the $SU(N{)}_1$ Wess-Zumino-Novikov-Witten conformal field theory for open boundary conditions. This has been achieved by extensive exact diagonalizations for $N$ between $3$ and $9$, and by a parton construction based on a set of $N$ Gutzwiller projected fermionic wave-functions with flux $\pi \mathrm{/}N$ per triangular plaquette. Experimental implications are briefly discussed.