Abstract
We consider the family of renormalizable scalar QFTs with self-interacting potentials of highest monomial ϕ m below their upper critical dimensions \( {d}_c=\frac{2m}{m-2} \), and study them using a combination of CFT constraints, Schwinger-Dyson equation and the free theory behavior at the upper critical dimension. For even integers m ≥ 4 these theories coincide with the Landau-Ginzburg description of multi-critical phenomena and interpolate with the unitary minimal models in d = 2, while for odd m the theories are non-unitary and start at m = 3 with the Lee-Yang universality class. For all the even potentials and for the Lee-Yang universality class, we show how the assumption of conformal invariance is enough to compute the scaling dimensions of the local operators ϕ k and of some families of structure constants in either the coupling’s or the ϵ-expansion. For all other odd potentials we express some scaling dimensions and structure constants in the coupling’s expansion.
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ArXiv ePrint: 1703.04830
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Codello, A., Safari, M., Vacca, G.P. et al. Leading CFT constraints on multi-critical models in d > 2. J. High Energ. Phys. 2017, 127 (2017). https://doi.org/10.1007/JHEP04(2017)127
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DOI: https://doi.org/10.1007/JHEP04(2017)127