The Orbifolds of Permutation-type as Physical String Systems at Multiples of C = 26 v. Cyclic Permutation Orbifolds

I consider the Z λ , λ prime free-bosonic permutation orbifolds as interacting physical string systems atˆc = 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.