The orbifolds of permutation-type as physical string systems at multiples of c = 26: I. Extended actions and new twisted world-sheet gravities

This is the first in a series of papers in which I investigate the orbifolds of permutation-type as candidates for new physical string systems at multiples of critical closed-string central charges. Examples include the bosonic orientation orbifolds, the bosonic permutation orbifolds and others, as well as superstring extensions. In this paper I use the extended (twisted) Virasoro algebras of these orbifolds to construct the corresponding extended action formulations of the twisted open- and closed-string sectors of all the bosonic orbifolds at c-circumflex = 26K. The extended actions exhibit a large set of new twisted world-sheet gravities, whose extended diffeomorphism groups clearly indicate that the associated operator-string theories can be free of negative-norm states at higher central charge