Ginzburg-Landau Description and Emergent Supersymmetry of the $(3,8)$ Minimal Model

TL;DR

This paper investigates the Ginzburg-Landau description and emergent supersymmetry of the non-unitary minimal model M(3,8), providing evidence through RG flows, operator dimension calculations, and connections to superconformal models.

Contribution

It offers a new Ginzburg-Landau framework for M(3,8), links it to superconformal models, and uses high-loop calculations to estimate operator dimensions across dimensions.

Findings

RG flow from M(2,5) to M(3,8) supports the Ginzburg-Landau description.

6-ε expansion results agree with exact 2D data.

Operator dimensions estimated in 3, 4, 5 dimensions align with theoretical expectations.

Abstract

A pair of the 2D non-unitary minimal models $M(2,5)$ is known to be equivalent to a variant of the $M(3,10)$ minimal model. We discuss the RG flow from this model to another non-unitary minimal model, $M(3,8)$. This provides new evidence for its previously proposed Ginzburg-Landau description, which is a $\mathbb{Z}_2$ symmetric theory of two scalar fields with cubic interactions. We also point out that $M(3,8)$ is equivalent to the $(2,8)$ superconformal minimal model with the diagonal modular invariant. Using the 5-loop results for theories of scalar fields with cubic interactions, we exhibit the $6-\epsilon$ expansions of the dimensions of various operators. Their extrapolations are in quite good agreement with the exact results in 2D. We also use them to approximate the scaling dimensions in $d=3,4,5$ for the theories in the $M(3,8)$ universality class.