Peculiarity of String Theory on Orbifolds in the Presence of an Antisymmetric Background Field

We study string theory on orbifolds in the presence of an antisymmetric constant background field and discuss some of new aspects of the theory. It is shown that the term with the antisymmetric field has a topological nature like a Chern-Simons term or a Wess-Zumino term. Due to this property, the theory exhibits various anomalous behavior: Zero mode variables obey nontrivial quantization conditions. Coordinate transformations which define orbifolds are modified at the quantum level. Wavefunctions of twisted strings acquire phase factors when they move around non-contractible loops on orbifolds. Zero mode eigenvalues are shifted from naively expected values, in favor of modular invariance.