Ginzburg-Landau description of a class of non-unitary minimal models

Abstract

It has been proposed that the Ginzburg-Landau description of the non-unitary conformal minimal model M (3, 8) is provided by the Euclidean theory of two real scalar fields with third-order interactions that have imaginary coefficients. The same lagrangian describes the non-unitary model M (3, 10), which is a product of two Yang-Lee theories M (2, 5), and the Renormalization Group flow from it to M (3, 8). This proposal has recently passed an important consistency check, due to Y. Nakayama and T. Tanaka, based on the anomaly matching for non-invertible topological lines. In this paper, we elaborate the earlier proposal and argue that the two-field theory describes the D series modular invariants of both M (3, 8) and M (3, 10). We further propose the Ginzburg-Landau descriptions of the entire class of D series minimal models M (q, 3q – 1) and M (q, 3q + 1), with odd integer q. They involve \( \mathcal{PT} \) symmetric theories of two scalar fields with interactions of order q multiplied by imaginary coupling constants.