Conjecture: Odd‑potential single‑field PT‑symmetric theories correspond to M(2, 2m+1)

Establish that, in two dimensions, the PT‑symmetric Euclidean scalar field theory with one real field φ and imaginary coupling to an odd interaction of the form g φ^{2m−1}/(2m−1)! has an infrared fixed point that realizes the non‑unitary minimal model M(2, 2m+1) for all integers m ≥ 2.

Background

The authors review the sequence of single‑field odd‑potential theories (beginning with the Yang–Lee iφ^3 model) that possess IR fixed points near their respective upper critical dimensions and have been proposed as GL descriptions of the M(2, 2m+1) minimal models.

This conjectural identification, supported by ε‑expansions and PT symmetry considerations, remains a standing question in the literature and serves as context for the paper’s extension to two‑field theories covering broader D‑series families.