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We show that the Fu-Kane-Mele invariant of the 2d time-reversal-invariantcrystalline insulators is equal to the properly normalized Wess-Zumino actionof the so-called sewing matrix field defined on the Brillouin torus. Applied to3d, the result permits a direct proof of the known relation between the strongFu-Kane-Mele invariant and the Chern-Simons action of the non-Abelian Berryconnection on the bundle of valence states.

2d Fu-Kane-Mele invariant as Wess-Zumino action of the sewing matrix