The orbifolds of permutation-type as physical string systems at multiples of c=26: III. The spectra of cˆ=52 strings

In the second paper of this series, I obtained the twisted BRST systems and extended physical-state conditions of all twisted open and closed cˆ=52 strings. In this paper, I supplement the extended physical-state conditions with the explicit form of the extended (twisted) Virasoro generators of all cˆ=52 strings, which allows us to discuss the physical spectra of these systems. Surprisingly, all the cˆ=52 spectra admit an equivalent description in terms of generically-unconventional Virasoro generators at c=26. This description strongly supports our prior conjecture that the cˆ=52 strings are free of negative-norm states, and moreover shows that the spectra of some of the simpler cases are equivalent to those of ordinary untwisted open and closed c=26 strings.