  In this paper, we study phase structure of $Z_2$ lattice gauge theories that
appear as an effective field theory describing low-energy properties of
frustrated antiferromagnets in two dimensions. Spin operators are expressed in
terms of Schwinger bosons, and an emergent U(1) gauge symmetry reduces to a
$Z_2$ gauge symmetry as a result of condensation of a bilinear operator of the
Schwinger boson describing a short-range spiral order. We investigated the
phase structure of the gauge theories by means of the Monte-Carlo simulations,
and found that there exist three phases, phase with a long-range spiral order,
a dimer state, and a spin liquid with deconfined spinons. Detailed phase
structure and properties of phase transitions depend on details of the models.
