GAUGE FIELD MASS GENERATION BY TOROIDAL SPACETIME

We consider an Abelian gauge field theory on the partially compactifie d spacetime T(N) x M, where T(N) is the N-dimensional torus and M is a n-dimensional Riemannian manifold. The mass of the gauge field genera ted by quantum fluctuations of a massive or massless scalar field, min imally coupled to a constant background gauge potential, is the quanti ty of our main interest. As long as the eigenvalue spectrum of -DELTA + xiR + m2 is positive (where DELTA is the Laplace-Beltrami operator o f the manifold M, R the Riemann scalar curvature and m the mass of the quantum field), it is found that the topologically generated mass is real for arbitrary N. If, however, the spectrum has zero eigenvalues w e found that, depending on the compactification lengths of the torus, the generated mass may also be imaginary.