One-Loop Renormalization and Asymptotic Behaviour of a Higher-Derivative Scalar Theory in Curved Spacetime

Abstract

A higher-derivative, interacting, scalar field theory in curved spacetime with the most general action of sigma-model type is studied. The one-loop counterterms of the general theory are found. The renormalization group equations corresponding to two different, multiplicatively renormalizable variants of the same are derived. The analysis of their asymptotic solutions shows that, depending on the sign of one of the coupling constants, we can construct an asymptotically free theory which is also asymptotically conformal invariant at strong (or small) curvature. The connection that can be established between one of the multiplicatively renormalizable variants of the theory and the effective theory of the conformal factor, aiming at the description of quantum gravity at large distances, is investigated.

11 pages, LaTeX file (some mistakes have been corrected and a reference has been added), UB-ECM-PF 94/5

References in corpus (4)

• A Cosmological Theory without Singularities
• Conformal Symmetry and Central Charges in 4 Dimensions
• Effective Potential for the Conformal Sector of Quantum Gravity with Torsion
• Conformal dynamics of quantum gravity with torsion

Cited by in corpus (23)

• Effective Field Theory for Inflation
• One loop renormalization of the four-dimensional theory for quantum dilaton gravity.
• Primordial backgrounds of relic gravitons
• Conformal Transformation in Gravity
• Auxiliary fields representation for modified gravity models
• On the inflationary solutions in higher-derivative gravity with dilaton field
• Renormalization group study of the higher derivative conformal scalar model
• Interaction of Low - Energy Induced Gravity with Quantized Matter and Phase Transition Induced by Curvature
• A Four-Dimensional Theory for Quantum Gravity with Conformal and Nonconformal Explicit Solutions
• Post-inflationary phases stiffer than radiation and Palatini formulation
• Renormalization group and logarithmic corrections to scaling relations in conformal sector of 4D gravity
• Running couplings and unitarity in a 4-derivative scalar field theory
• An effective theory of accelerated expansion
• Averaged Energy Conditions and Bouncing Universes
• Higher Order Lagrangians inspired by the Pais-Uhlenbeck Oscillator and their cosmological applications
• Stringy bounces and gradient instabilities
• Quantum dynamics of N=1, D=4 supergravity chiral compensator
• S-matrix Unitarity and Renormalizability in Higher Derivative Theories
• Palatini approach and large-scale magnetogenesis
• Effective approach to the Antoniadis-Mottola model: quantum decoupling of the higher derivative terms
• Interaction of Low - Energy Induced Gravity with Quantized Matter -- II. Temperature effects
• FeynGrav 3.0
• Gravitational wave from cosmic inflation in a gravity with two small four-derivative corrections