Emergence of dynamical tensor fields in composite models of gravity
Yadikaer Maitiniyazi, Masatoshi Yamada
TL;DR
This paper investigates the emergence of dynamical tensor fields in composite gravity models using the functional Renormalization Group. It analyzes two sectors—a fermionic and a scalar model—each augmented by an auxiliary tensor field through the Hubbard-Stratonovich transformation, and derives flow equations for the associated mass and kinetic terms. Quantum fluctuations generate finite, IR-dynamical kinetic terms for these tensor fields, which can be interpreted as gauge-fixed diffeomorphism-invariant dynamics rather than fully covariant Einstein gravity. The results establish a framework for understanding emergent gravity from composite degrees of freedom and point to future work on higher-order vertices and dynamical bosonization to refine gravitational interactions. Overall, the work demonstrates a concrete route to an emergent graviton within a controlled quantum-field-theoretic setting and outlines the steps needed to advance toward a complete composite theory of gravity.
Abstract
We study the composite models of gravity and investigate how dynamical tensor fields emerge by utilizing the functional Renormalization Group. In this paper, we consider two models: One is the fermionic theory. Another is the scalar theory. In both cases, we introduce an auxiliary tensor field corresponding to a composite field of the energy-momentum tensor by means of the Hubbard-Stratonovich transformation. We derive the flow equations for the field renormalization factors of the auxiliary tensor field and show the tensor field becomes dynamical in the infrared regime. The resulting kinetic terms are interpreted as gauge-fixed terms.