We consider the phase structure of the linear quiver gauge theory, using the
't Hooft anomaly matching condition. This theory is characterized by the length
K of the quiver diagram. When K is even, the symmetry and its anomaly are
the same as those of massless QCD. Therefore, one can expect that the
spontaneous symmetry breaking similar to the chiral symmetry breaking occurs.
On the other hand, when K is odd, the anomaly matching condition is satisfied
by the massless composite fermions. We also consider the thermal partition
function under the twisted boundary conditions. When K is even, from the
anomaly at finite temperature, we estimate the relation between the critical
temperatures associated with the confinement/deconfinement and the breaking of
the global symmetry. Finally we discuss the anomaly matching at finite
temperature when K is odd.Comment: 20 pages, 6 figure