A Renormalization Group Analysis of the Ising Model Coupled to Causal Dynamical Triangulations

Abstract

We analyze the matrix model characterizing the Ising model coupled to Causal Dynamical Triangulations (CDT) from the point of view of the Functional Renormalization Group Equation (FRGE). This model is a dually weighted matrix model, whose Feynman diagrams are in correspondence with discrete triangulations of two-dimensional geometries with a preferred time foliation. In particular, we find the fixed points of the beta-function equations, showing that the number of relevant directions in each case is compatible with the physical interpretation of the CFT at the fixed point. In addition to recovering the fixed points for topological gravity and pure gravity with a cosmological constant, we find a new fixed point featuring three relevant directions which matches the number of primary fields in the Ising CFT.

23 pages, 2 figures; v.3 Version published on JHEP

References in corpus (21)

• Exact evolution equation for the effective potential
• 2D Gravity and Random Matrices
• Spectral Dimension of the Universe
• Reconstructing the Universe
• Non-perturbative Lorentzian Quantum Gravity, Causality and Topology Change
• Planckian Birth of the Quantum de Sitter Universe
• The Universe from Scratch
• Continuum limit in matrix models for quantum gravity from the Functional Renormalization Group
• 2d CDT is 2d Horava-Lifshitz quantum gravity
• A new perspective on matter coupling in 2d quantum gravity
• The Virasoro Minimal String
• On the spectral dimension of causal triangulations
• Shaken, but not stirred - Potts model coupled to quantum gravity
• Crossing the c=1 barrier in 2d Lorentzian quantum gravity
• Notes on Matrix Models
• Imposing causality on a matrix model
• The complex Liouville string: the matrix integral
• The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization
• A c=1 phase transition in two-dimensional CDT/Horava-Lifshitz gravity?
• The cylinder amplitude in the Hard Dimer model on 2D Causal Dynamical Triangulations
• Conformal Dimensions On Causal Random Geometry