T-DUALITY OF PERTURBATIVE CHARACTERS FOR CLOSED BOSONIC AND TYPE-II STRING THEORIES

A systematic study of duality properties of string characters associat ed with the transverse space-time rotations is undertaken. Although ye t restricted to the perturbative spectrum, our work shows that these c haracters, already considered earlier as a book-keeping device for the free string quantum numbers, are useful tools in connection with the current developments of string duality ideas. In particular, the O(8) triality properties of the characters for critical superstrings, show that there exists a third formulation (unnoticed so far to our knowled ge) equivalent to, but different from the ones of Neveu-Schwarz-Ramond , and Green-Schwarz. For the bosonic modes, modular invariance require s that one also takes the trace over the total momentum, in contrast t o what was done earlier. Although we do not consider supercharacters, the consequences of supersymmetry are neatly derived at once for all m assive states by factorizing the character of the long SUSY multiplet. (C) 1998 Elsevier Science B.V.