The large-scale vortex structures under spilling and plunging breakers are investigated, using a fully three-dimensional large-eddy simulation (LES). When an overturning jet projecting from the crest in a breaking wave rebounds from the water surface ahead, the vorticity becomes unstable in a saddle region of strain between the rebounding jet and a primary spanwise vortex, resulting in spanwise undulations of the vorticity. The undulations are amplified on a braid in this saddle region, leading to a vortex loop with counter-rotating vorticity. This vortex loop consequently envelops adjacent primary vortices, to form a typical rib structure. This rib component (the stretched vortex loop) in the large-scale vortex structure, which intensifies in the strains associated with the multiple primary vortices generated throughout the splash-up cycle, appears to be the previously found obliquely descending eddy.