Renormalization group fixed points of foliated gravity-matter systems

Understand

We employ the Arnowitt-Deser-Misner formalism to study the renormalization group flow of gravity minimally coupled to an arbitrary number of scalar, vector, and Dirac fields.

• The decomposition of the gravitational degrees of freedom into a lapse function, shift vector, and spatial metric equips spacetime with a preferred (Euclidean) "time"-direction.
• In this work, we provide a detailed derivation of the renormalization group flow of Newton's constant and the cosmological constant on a flat Friedmann-Robertson-Walker background.
• Adding matter fields, it is shown that their contribution to the flow is the same as in the covariant formulation and can be captured by two parameters $d_g$, $d_\lambda$.