Renormalization of multicritical scalar models in curved space

TL;DR

This paper studies the renormalization of multicritical scalar field models in curved space, focusing on the nonminimal coupling to curvature and its fixed points, with implications for two-dimensional gravity.

Contribution

It provides a perturbative renormalization analysis of $ ext{phi}^{2n}$ models in curved space, highlighting the conformal coupling fixed point and its relation to two-dimensional gravity.

Findings

Identification of the conformal value of the nonminimal coupling $\xi$ as a fixed point.

Analysis of the beta function behavior at and below the upper critical dimension.

Connection of results with Kawai and Ninomiya's two-dimensional gravity formulation.

Abstract

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