Renormalization of multicritical scalar models in curved space

Abstract

Abstract We consider the leading order perturbative renormalization of the multicritical $$\phi ^{2n}$$ ϕ2n models and some generalizations in curved space. We pay particular attention to the nonminimal interaction with the scalar curvature $$\frac{1}{2}\xi \phi ^2 R$$ 12ξϕ2R and discuss the emergence of the conformal value of the coupling $$\xi $$ ξ as the renormalization group fixed point of its beta function at and below the upper critical dimension as a function of n. We also examine our results in relation with Kawai and Ninomiya’s formulation of two dimensional gravity.