We establish the functional renormalization group as an exploratory tool to investigate a possible phase transition between a pregeometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the analysis of Eichhorn and Koslowski [Phys. Rev. D 88, 0840156 (2013)], we study three new aspects of the double-scaling limit of matrix models as renormalization group fixed points. First, we investigate multicritical fixed points, which are associated with quantum gravity coupled to conformal matter. Second, we discuss an approximation that reduces the scheme dependence of our results as well as computational effort while giving good numerical results. This is a consequence of the approximation being a solution to the unitary Ward identity associated to the U(N) symmetry of the Hermitian matrix model. Third, we discuss a scenario that relates the double-scaling limit to fixed points of continuum quantum gravity.
|Journal||Physical Review D - Particles, Fields, Gravitation and Cosmology|
|Publication status||Published - 2014|