Renormalization of multicritical scalar models in curved space

Abstract

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

arXiv comment13 pages, 3 figures; v3: matches the published version

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Cited by in corpus (5)

• Vacuum effective actions and mass-dependent renormalization in curved space
• Gravity in $d=2+\epsilon$ dimensions and realizations of the diffeomorphisms group
• Symmetry and universality of multi-field interactions in $6-\epsilon$ dimensions
• Non-perturbative quantum Galileon in the exact renormalization group
• Pauli-Term-Induced Fixed Points in $d$-dimensional QED