Topological Aspects of an Antisymmetric Background Field on Orbifolds

We study string theory on orbifolds in the presence of an antisymmetric constant background field in detail and discuss some of new aspects of the theory. It is pointed out that the term with the antisymmetric background field can be regarded as a topological term like a Chern-Simons term or a Wess-Zumino term. Detailed analysis in the operator formalism shows that orbifold models with topologically nontrivial twists exhibit various anomalous behavior: Zero mode variables obey nontrivial quantization conditions. Coordinate transformations which define orbifolds are modified at quantum level. Wave functions of twisted strings in general acquire nontrivial phases when they move around non-contractible loops on orbifolds. Zero mode eigenvalues are shifted from naively expected values, in favor of modular invariance.