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

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.

24 pages, 2 figures; v3: additional symmetry constraints pointed out, references added

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Cited by in corpus (5)

• Effective Hamiltonians and Counterterms for Hamiltonian Truncation
• Testing the RG-flow $M(3,10)+{\varphi }_{1,7}\to M(3,8)$ with Hamiltonian Truncation
• The fate of non-supersymmetric Gross-Neveu-Yukawa fixed point in two dimensions
• Minimal Models RG flows: non-invertible symmetries & non-perturbative description
• Sphere free energy of scalar field theories with cubic interactions