  We consider the Abelian Higgs model in a (p+2)-dimensional space time with
topology M^{p+1} x S^1 as a field theoretical toy model for tachyon
condensation on Dp-branes. The theory has periodic sphaleron solutions with the
normal mode equations resembling Lame-type equations. These equations are
quasi-exactly solvable (QES) for specific choices of the Higgs- to gauge boson
mass ratio and hence a finite number of algebraic normal modes can be computed
explicitely. We calculate the tachyon potential for two different values of the
Higgs- to gauge boson mass ratio and show that in comparison to previously
studied pure scalar field models an exact cancellation between the negative
energy contribution at the minimum of the tachyon potential and the brane
tension is possible for the simplest truncation in the expansion about the
field around the sphaleron. This gives further evidence for the correctness of
Sen's conjecture.
