A<sc>bstract</sc> It has been proposed that the Ginzburg-Landau description of the non-unitary conformal minimal modelM(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 modelM(3, 10), which is a product of two Yang-Lee theoriesM(2, 5), and the Renormalization Group flow from it toM(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 theDseries modular invariants of bothM(3, 8) andM(3, 10). We further propose the Ginzburg-Landau descriptions of the entire class ofDseries minimal modelsM(q, 3q– 1) andM(q, 3q+ 1), with odd integerq. They involve$$ \mathcal{PT} $$ symmetric theories of two scalar fields with interactions of orderqmultiplied by imaginary coupling constants.
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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.
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- Award ID(s):
- 2209997
- PAR ID:
- 10428495
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2023
- Issue:
- 2
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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