  The observed mass pattern of scalar resonances below 1 GeV gives preference
to the tetraquark assignment over the conventional $\bar qq$ assignment for
these states. We present a search for tetraquarks with isospins 0,1/2,1 in
lattice QCD, where isospin channels 1/2 and 1 have not been studied before. Our
simulation uses Chirally Improved fermions on quenched gauge configurations. We
determine three energy levels for each isospin using the variational method.
The ground state is consistent with the scattering state, while the two excited
states have energy above 2 GeV. Therefore we find no indication for light
tetraquarks at our range of pion masses 344-576 MeV.
