Modular invariance of some fermionic theories and their bosonized versions

Abstract

String theories with N free Majorana or massless Dirac fermions are considered. The different possible modular invariant truncations are listed in each case. The spectrum of these theories is compared to the semiclassical spectrum of their bosonized versions, which are theories of strings moving on the group manifolds of SO( N) or spin ( N) for the Majorana case, and of U( N) for the Dirac case, with the coefficient of the WZW term equal to its minimum nonzero value in both cases. In doing this, a better understanding of bosonization and of the exact sense in which it is valid is sought.