Partial-Symmetry-Breaking Phase Transitions

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.