General unknown: Ginzburg–Landau descriptions for most non‑unitary minimal models

Determine Ginzburg–Landau effective field theory descriptions for the non‑unitary Virasoro minimal models M(p, q) that currently lack such descriptions, specifying for each model the appropriate field content, interactions, and symmetry structure that reproduce its operator spectrum and RG behavior in two dimensions.

Background

The paper surveys known Ginzburg–Landau (GL) descriptions of certain non‑unitary minimal models, including single‑field odd‑potential theories conjectured to describe M(2, 2m+1) and a two‑field cubic theory proposed for M(3,8) and M(3,10). It emphasizes that, despite recent progress, large portions of the non‑unitary landscape remain without GL realizations.

This broad unknown motivates the authors’ program to extend two‑field GL constructions (with imaginary couplings and PT symmetry) to entire D‑series families M(q, 3q−1) and M(q, 3q+1) for odd q, but beyond these classes many models still lack identified GL theories.