  We present an analytic nonperturbative solution of the Yakubovsky equation
for tetraquark states in the case of equal separations and energies, and
demonstrate a direct connection between the tetraquark confinement potential
and the temporal gluon propagator. To this end we employ a leading-order heavy
quark mass expansion of the Coulomb gauge QCD action, and use the dressed
two-point functions of the Yang-Mills sector only. As a result we find a bound
state energy that rises linear with distance and a string tension twice as
large as in a $q\bar{q}$-system.
