  There has been substantial progress in understanding a class of SU(N) gauge
theories that are confining at high temperatures. This class includes theories
with center-symmetric Polyakov loop deformations or with periodic adjoint
fermions. The crucial role of monopoles in lattice gauge theories of this type
can be understood analytically. The basic mechanisms occur in the
two-dimensional O(3) spin model, deformed by appropriate mass term to give an
XY model. Vortices of the XY model are constituents of O(3) instantons just as
SU(N) magnetic monopoles are constituents of KvBLL instantons. Similar methods
applied to an SU(2) lattice gauge theory yield an effective U(1) description in
which monopoles are responsible for confinement.
