TOPOLOGICAL GAUGE FIELD MASS GENERATION BY TOROIDAL SPACETIME

We consider an Abelian gauge field theory on Euclidean partially compa ctified spacetime T(N) x R(n) for arbitrary N and n. The one-loop effe ctive potential generated by quantum fluctuations of a massive scalar field, minimally coupled to a constant background Abelian gauge potent ial is calculated for arbitrary compactification lengths L1, ..., L(N) Of the multi-dimensional torus. In particular the topologically gener ated mass of the gauge field is obtained and its complicated dependenc e on the parameters involved (compactification lengths, mass M of the scalar field) is given explicitly. It is found that the topologically generated mass is positive for arbitrary N and n and that it does not depend on a renormalization parameter. For n > 2 the limit M --> 0 is smooth, but for n = 0, 1, 2 zero modes play a crucial role and the gen eration of real or imaginary gauge field masses is possible.