Continuum description of the self-dual critical point in 3D Z2 gauge theory with matter

Develop a useful continuum field-theoretic description of the phase transition at the self-dual point in three-dimensional Z2 lattice gauge theory with matter, which exhibits Higgs–confinement continuity and a self-duality symmetry. The goal is to construct or identify a continuum critical theory capturing the universal properties at this self-dual transition.

Background

In the discussion of 3D Z2 lattice gauge theory with matter, the authors outline a phase diagram featuring a topological (deconfined) phase and a phase continuously connected to both Higgs and confined regimes, illustrating Higgs/confinement continuity. They note the presence of a self-duality symmetry that maps the two sides of the phase diagram to each other and refer to work analyzing the physics at the self-dual point.

Despite progress in numerical and lattice studies, the authors indicate that a useful continuum field-theoretic description of the critical behavior at this self-dual transition point is not currently available. Such a description would provide an analytic understanding of one of the simplest beyond-Landau critical points, potentially clarifying universal features and critical exponents.