Abstract
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.
Highlights
In this paper, we suggest a generic feature of the phase transitions in local quantum field theories with large rank symmetry groups and all-to-all couplings between internal degrees of freedom
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
To further clarify the language that we will be using throughout the paper, we will refer to the background spacetime on which local physics takes place as physical space and the background on which the degrees of freedom experience all-to-all coupling as internal space
Summary
We suggest a generic feature of the phase transitions in local quantum field theories with large rank symmetry groups and all-to-all couplings between internal degrees of freedom. At the critical temperature T 1⁄4 Tc 1⁄4 0 °C, water goes through a first-order transition, and the liquid and solid phases can coexist in physical space. Associated with the first-order transition, metastable phases such as supercooled liquid and superheated solid can appear Such metastable phases due to the local interaction are unstable to a small perturbation, even in the thermodynamic (large-volume) limit. We will provide a brief recap, discussion, and outlook for future work
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