General Ginzburg–Landau description of M(2,2n+1) via iφ^{2n−1} interactions

Establish in two dimensions that, for every integer n ≥ 2, the non-unitary minimal model M(2, 2n+1) is described by the massless Euclidean scalar Ginzburg–Landau field theory with action S = ∫ d^d x [ (1/2)(∂_μ φ)^2 + g φ^{2n−1}/(2n−1)! ] and purely imaginary coupling g ∈ iℝ, thereby providing a general iφ^{2n−1} Ginzburg–Landau description of all M(2, 2n+1) minimal models.

Background

The paper argues that the quintic PT-symmetric scalar theory with action S = ∫ d^d x [ (1/2)(∂φ)^2 + g φ^5/120 ], g ∈ iℝ, matches the two-dimensional minimal model M(2,7), extending the well-established identification of the cubic iφ^3 theory with M(2,5). Motivated by PT symmetry and operator-product-expansion patterns across these cases, the authors propose a unified Ginzburg–Landau description for the entire family M(2, 2n+1).

They note that the minimal models M(2, 2n+1) exhibit PT symmetry and lack a Z2 symmetry, mirroring scalar theories with odd potentials iφ^{2n−1}. Building on these structural similarities and successful two-sided Padé extrapolations, they conjecture a general action S_{2,2n+1} with iφ^{2n−1} interaction, and remark that OPE checks appear promising while leaving detailed validation for future work.