Ginzburg-Landau description of non-unitary minimal models

In two dimensions, minimal models provide an infinite class of conformal field theories where all physical properties are known, including dimensions of operators and, at least in principle, correlation functions. However, the vast majority of these models have no known explicit description in terms of a Ginzburg-Landau field theory. Understanding this requires analyzing very strongly coupled field theories. We will provide strong arguments that give a new Lagrangian field theory description to a non-unitary minimal model, using mainly symmetry and novel c-theorem arguments. We will also see that specifically in two dimensions, this simple bosonic statistical system is constrained at criticality by an unexpectedly emergent supersymmetry.