Partial-symmetry-breaking phase transitions

Abstract

We demonstrate a novel feature of certain phase transitions in theories with large rank symmetry group that exhibit specific types of all-to-all interactions, a typical example being the matrix model description of a large-N gauge theory. 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 all-to-all interaction. In this article, we show that similar phase transitions with partially broken symmetry can exist in various examples from quantum field theory 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. In some of these examples, we give new interpretations to previously known solutions and clarify the underlying physical mechanism governing their phase behavior.