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

TL;DR

This paper extends the Ginzburg-Landau framework to describe a broad class of non-unitary minimal models, specifically the D series, using PT-symmetric two-scalar field theories with imaginary interactions.

Contribution

It generalizes the Ginzburg-Landau description to all D series minimal models M(q, 3q±1) with odd q, involving PT-symmetric scalar field theories with higher-order imaginary interactions.

Findings

The two-field theory describes D series modular invariants of M(3,8) and M(3,10).

Proposes Ginzburg-Landau descriptions for entire D series minimal models.

Validates the approach through consistency with anomaly matching and topological line analysis.

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 $PT$ symmetric theories of two scalar fields with interactions of order $q$ multiplied by imaginary coupling constants.