A survey of large N continuum phase transitions
R. Narayanan, H. Neuberger
TL;DR
This survey compiles the landscape of large $N$ continuum phase transitions across $d=2$--$4$, emphasizing continuum reduction, Wilson loop universality, and a cascade of center-symmetry breakings on toroidal geometries. It highlights analytic and lattice results for DO and DO-like transitions, Gross–Witten transitions, and the double scaling universal function given by a Generalized Airy integral, while extending these ideas to 3d and 4d via twisted Eguchi–Kawai, adjoint matter, and finite-volume analyses. The work also discusses topological aspects (the $\theta$ parameter), chiral dynamics in the large $N$ limit, and connections to gravity and string theory through phase-cascade analogies such as Gregory–Laflamme transitions. Together, these results illuminate how large $N$ gauge theories exhibit volume independence or controlled finite-volume behavior in certain phases, while providing concrete scaling laws and universal structures that inform continuum limits and potential holographic connections.
Abstract
The main focus of this talk is the physics of large N QCD on a continuum torus. A cascade of phase transitions associated with the breaking of U(1) symmetries will be discussed. The continuum Wilson loop as a function of its area will be discussed along with its universality properties and the associated double scaling limit. Some recent progress in twisted Eguchi-Kawai is presented. Gauge field topology and $θ$ vacuua are also discussed in the context of large N gauge theories. Phase transitions in 2D large N principal chiral models are compared with similar transitions in large $N$ gauge theories. Finally, connections to some topics in string theory and gravity are briefly described.