The generalized Casimir operator Ω is the only known polynomial element of the center Z of the universal enveloping algebra U(𝔤) of an indefinite Kac–Moody algebra 𝔤. However, Kac [115Jump To The Next Citation Point] has proven the existence of higher order non-polynomial Casimir operators which are elements of the center Z𝔉 of a suitable completion U𝔉(𝔤) of the universal enveloping algebra of 𝔤. Recently, an explicit physics-inspired construction was made, following [115], for affine 𝔤 in terms of Wilson loops for WZW-models [1].