Remarkable formulae for the tree-level S-matrix of gauge and gravity theories were recently discovered by Cachazo-He-Yuan, based on a localisation procedure in the moduli space of Riemann surfaces. These formulae are now known to arise from new string-like chiral models. These naturally produces loop-level amplitudes, also localised in the moduli space of higher genus curves. However, the resolution of the localisation equations is immensely more difficult than at tree-level, and it remained as an open question as to what these formulae computed, and more generally if these string models made sense at the quantum level. In this talk I'll describe a resolution of the localisation equations at one-loop in a particular kinematical regime, and show agreement with known amplitudes. Then I'll describe a much more powerful method, based on an integration by parts which degenerates the torus down to a sphere (plus two new points). The model is then solved like at tree-level. I'll briefly discuss extension to higher loops in conclusion.