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Renormalization group flows and fixed points for a scalar field in curved space with nonminimal F(φ)R coupling

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arxiv 1711.02224 v1 pith:67VVR4W4 submitted 2017-11-06 hep-th

Renormalization group flows and fixed points for a scalar field in curved space with nonminimal F(φ)R coupling

Boris S. Merzlikin , Ilya L. Shapiro , Andreas Wipf , Omar Zanusso This is my paper
classification hep-th
keywords couplingfixednon-minimalrenormalizationscalarcurvedfieldgroup
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Using covariant methods, we construct and explore the Wetterich equation for a non-minimal coupling $F(\phi)R$ of a quantized scalar field to the Ricci scalar of a prescribed curved space. This includes the often considered non-minimal coupling $\xi \phi^2 R$ as a special case. We consider the truncations without and with scale- and field-dependent wave function renormalization in dimensions between four and two. Thereby the main emphasis is on analytic and numerical solutions of the fixed point equations and the behavior in the vicinity of the corresponding fixed points. We determine the non-minimal coupling in the symmetric and spontaneously broken phases with vanishing and non-vanishing average fields, respectively. Using functional perturbative renormalization group methods, we discuss the leading universal contributions to the RG flow below the upper critical dimension $d=4$.

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Cited by 3 Pith papers

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    UV completeness in scalar-tensor gravity restricts Yukawa fifth-force parameters α and λ to a finite wedge whose complement is ruled out, with part of the excluded domain below current experimental bounds.

  3. Gravitationally Induced UV Completion of an $O(N)$ Scalar Theory

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    Gravity's non-minimal coupling drives the quartic self-coupling of an O(N) scalar to zero at an attractive fixed point, making the broken-phase theory UV-complete and bounding the scalar mass.