Ginzburg-Landau description and emergent supersymmetry of the (3, 8) minimal model

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 ℤ₂ 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 − ϵ 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.