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

Abstract

We consider the family of renormalizable scalar QFTs with self-interacting potentials of highest monomial ${\varphi }^m$ 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 $m\ge 4$ 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 ${\varphi }^k$ and of some families of structure constants in either the coupling's or the $\epsilon$-expansion. For all other odd potentials we express some scaling dimensions and structure constants in the coupling's expansion.

29 pages, 1 figure; V2: references added, minor improvements, to appear in JHEP

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• New universality class in three dimensions: The critical Blume-Capel model
• Scale and Conformal Invariance in Higher Derivative Shift Symmetric Theories
• Towards a Bootstrap approach to higher orders of epsilon expansion
• Leading order CFT analysis of multi-scalar theories in d>2
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