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

A bstract 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 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 − 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.