Emergence of dynamical tensor fields in composite models of gravity

Abstract

We investigate composite models of gravity and explore how dynamical tensor fields can emerge within the functional renormalization group framework. We consider two prototype models: a fermionic theory and a scalar theory. In both cases, an auxiliary tensor field is introduced via a Hubbard-Stratonovich transformation, corresponding to the composite channel associated with the energy-momentum tensor. We derive the flow equations for the field renormalization factors of the auxiliary tensor field and demonstrate that finite kinetic terms are dynamically generated in the infrared regime. Agreement with the diffeomorphism-invariant quadratic Einstein-Hilbert structure can be established in the transverse-traceless spin-2 sector, while the remaining contributions reside in the longitudinal and trace sectors. Although these terms can be cast into a form reminiscent of gauge-fixed presentations of the quadratic Einstein-Hilbert action, we do not interpret them as originating from a genuine gauge-fixing procedure within the present truncation.

7 pages, 1 figure

References in corpus (25)

• Exact evolution equation for the effective potential
• The Exact Renormalisation Group and Approximate Solutions
• Aspects of the Functional Renormalisation Group
• Optimised Renormalisation Group Flows
• The QCD phase structure at finite temperature and density
• Flow Equations for N Point Functions and Bound States
• Chiral symmetry breaking in continuum QCD
• Non-perturbative quark, gluon and meson correlators of unquenched QCD
• Renormalization Flow of Bound States
• From Quarks and Gluons to Hadrons: Chiral Symmetry Breaking in Dynamical QCD
• Universality of spontaneous chiral symmetry breaking in gauge theories
• Exact flow equation for composite operators
• Non-perturbative finite-temperature Yang-Mills theory
• Gravity from Spinors
• Spinor Gravity
• Bound state properties from the Functional Renormalisation Group
• On the origin of the difference between time and space
• Pregeometry and spontaneous time-space asymmetry
• Partial bosonisation for the two-dimensional Hubbard model: How well does it work?
• Pregeometry and euclidean quantum gravity
• Dynamically emergent gravity from hidden local Lorentz symmetry
• Gravity from symmetry breaking phase transition
• Irreversible vierbein postulate: Emergence of spacetime from quantum phase transition
• Spacetime and Planck mass generation from scale-invariant degenerate gravity
• Functional renormalization group study of a four-fermion model with $CP$ violation