  We propose a string theory construction for the system of two heavy quarks
and two light antiquarks. The potential of the system is a function of
separation between the quarks. We define a critical separation distance below
which the system can be thought of mainly as a compact tetraquark. The results
show the universality of the string tension and factorization at small
separations expected from heavy quark-diquark symmetry. Our estimate of the
screening length is in the range of lattice QCD. We also make a comparison with
the potential of the $QQq$ system. The potentials look very similar at small
quark separations but at larger separations they differ. The reason for this is
that the flattening of the potentials happens at two well-separated scales as
follows from the two different mechanisms: string breaking by light quarks for
$QQq$ and string junction annihilation for $QQ\bar q\bar q$. Moreover, a
similar construction can also be applied to the $\bar Q\bar Q qq$ system.
