Identify the E6 simple lines as Wilson loops

Identify the multinomial ultraviolet line operators appearing in the $E_6$ trace-formula theories as explicit supersymmetric Wilson loops, or otherwise determine their precise ultraviolet realization, so that the corresponding infrared simple-line interpretation is established.

Background

For the $E_6$ examples, the algorithm finds candidate simple lines whose expressions include multinomial combinations of Wilson-loop monomials. The paper permits such multinomial descriptions when no monomial Wilson loop satisfies the required modular-data constraints.

However, the physical identification of these multinomial operators as genuine supersymmetric Wilson loops is not established. Resolving this issue would clarify how the ultraviolet line-operator description realizes the simple objects of the infrared TQFT.