  We address the question whether the lightest scalar mesons sigma and kappa
are tetraquarks. We present a search for possible light tetraquark states with
J^PC=0^++ and I=0, 1/2, 3/2, 2 in the dynamical and the quenched lattice
simulations using tetraquark interpolators. In all the channels, we unavoidably
find lowest scattering states pi(k)pi(-k) or K(k)pi(-k) with back-to-back
momentum k=0,2*pi/L,.. . However, we find an additional light state in the I=0
and I=1/2 channels, which may be related to the observed resonances sigma and
kappa with a strong tetraquark component. In the exotic repulsive channels I=2
and I=3/2, where no resonance is observed, we find no light state in addition
to the scattering states.
