# Leading CFT constraints on multi-critical models in d > 2

Journal of High Energy Physics, Apr 2017

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.

This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2FJHEP04%282017%29127.pdf

Alessandro Codello, Mahmoud Safari, Gian Paolo Vacca, Omar Zanusso. Leading CFT constraints on multi-critical models in d > 2, Journal of High Energy Physics, 2017, 127, DOI: 10.1007/JHEP04(2017)127