  We demonstrate a novel feature of certain phase transitions in theories with
large rank symmetry group that exhibit specific types of non-local
interactions. A typical example of such a theory is a large-$N$ gauge theory
where by `non-local interaction' we mean the all-to-all coupling of color
degrees of freedom. Recently it has been pointed out that nontrivial features
of the confinement/deconfinement transition are understood as consequences of
the coexistence of the confined and deconfined phases on the group manifold
describing the color degrees of freedom. While these novel features of the
confinement/deconfinement transition are analogous to the two-phase coexistence
at the first order transition of more familiar local theories, various
differences such as the partial breaking of the symmetry group appear due to
the non-local interaction. In this article, we show that similar phase
transitions with partially broken symmetry can exist in various examples from
QFT and string theory. Our examples include the deconfinement and chiral
transition in QCD, Gross-Witten-Wadia transition in two-dimensional lattice
gauge theory, Douglas-Kazakov transition in two-dimensional gauge theory on
sphere, and black hole/black string transition.
