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arXiv · 2410.11714

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

Andrei Katsevich·Igor R. Klebanov·Zimo Sun
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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.

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Andrei Katsevich, Igor R. Klebanov, Zimo Sun. 2024-10-15. Ginzburg-Landau description of a class of non-unitary minimal models. https://arxiv.org/abs/2410.11714

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