Renormalization of multicritical scalar models in curved space

Abstract

We consider the leading order perturbative renormalization of the multicritical $ϕ^{2n}$ models and some generalizations in curved space. We pay particular attention to the nonminimal interaction with the scalar curvature $\frac{1}{2}ξϕ^2 R$ and discuss the emergence of the conformal value of the coupling $ξ$ 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.

13 pages, 3 figures; v3: matches the published version