Fractional Hall physics from large <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math> interacting fermions

We solve models of N species of fermions in the lowest Landau level with U(N)-invariant interactions in the N≫1 limit. We find saddles of the second quantized path integral at fixed chemical potential corresponding to fractional Hall states with filling (p/q), where the integers p and q depend on the chemical potential and interactions. On a long torus there are q such states related by translation symmetry, and SU(N)-invariant excitations of fractional charge. Remarkably, these saddles and their filling persist as extrema of the second-quantized action at N=1. Our construction gives a first-principles derivation of fractional Hall states from strongly interacting fermions.