2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/192572I consider the $\mathbb{Z}_λ,$ $λ$ prime free-bosonic permutation orbifolds as interacting physical string systems at $\hat{c} = 26λ$. As a first step, I introduce twisted tree diagrams which confirm at the interacting level that the physical spectrum of each twisted sector is equivalent to that of an ordinary $c=26$ closed string. The untwisted sectors are surprisingly more difficult to understand, and there are subtleties in the sewing of the loops, but I am able to propose provisional forms for the full modular-invariant cosmological constants and one-loop diagrams with insertions.46 pages, 4 figuresHigh Energy Physics - TheoryMathematical Physicstext