Constant field strengths on T-2n

We analyse field strength configurations in U(N) Yang-Mills theory on T-2n that are diagonal and constant, extending early work; of Van Baal on T-4. T he spectrum of fluctuations is determined and the eigenfunctions are given explicitly in terms of. theta functions on tori. We show the relevance of t he analysis to higher dimensional D-branes and discuss applications of the results in string theory. (C) 2000 Elsevier Science B.V. All rights reserve d.