Stochastic dynamics for Group Field Theories

Abstract

Phase transitions with spontaneous symmetry breaking are expected for group field theories as a basic feature of the geometogenesis scenario. The following paper aims to investigate the equilibrium phase for group field theory by using the ergodic hypothesis on which the Gibbs-Boltzmann distributions must break down. The breaking of the ergodicity can be considered dynamically, by introducing a fictitious time inducing a stochastic process described through a Langevin equation, from which the randomness of the tensor field will be a consequence. This type of equation is considered particularly for complex just-renormalizable Abelian model of rank d = 5, and we study some of their properties by using a renormalization group considering a coarse-graining both in time and space.

70 pages, 18 figures

References in corpus (26)

• Fluctuation-Dissipation: Response Theory in Statistical Physics
• A Short Review of Loop Quantum Gravity
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics: Real-time RG in frequency space (RTRG-FS)
• Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
• Symmetries of generating functionals of Langevin processes with colored multiplicative noise
• Thermal time and the Tolman-Ehrenfest effect: temperature as the "speed of time"
• Invitation to Random Tensors
• Group field theories for all loop quantum gravity
• Quantum cosmology from quantum gravity condensates: cosmological variables and lattice-refined dynamics
• Critical behavior in spherical and hyperbolic spaces
• Towards phase transitions between discrete and continuum quantum spacetime from the Renormalization Group
• Frequency regulators for the nonperturbative renormalization group: A general study and the model A as a benchmark
• Discrete Renormalization Group for SU(2) Tensorial Group Field Theory
• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
• Flow Equation for Supersymmetric Quantum Mechanics
• Group Field Theory in dimension four minus epsilon
• Emergent Cosmology from Quantum Gravity in the Lorentzian Barrett-Crane Tensorial Group Field Theory Model
• Dynamics of anisotropies close to a cosmological bounce in quantum gravity
• Effective dynamics of scalar cosmological perturbations from quantum gravity
• Phase transitions in TGFT: Functional renormalization group in the cyclic-melonic potential approximation and equivalence to O$(N)$ models
• The regulator dependence in the functional renormalization group: a quantitative explanation
• Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom
• Functional renormalization group for multilinear disordered Langevin dynamics I: Formalism and first numerical investigations at equilibrium
• No Ward-Takahashi identity violation for an Abelian tensorial group field theories with closure constraint
• Coarse-graining in time with the Functional Renormalisation Group: Relaxation in Brownian Motion

Cited by in corpus (5)

• Functional renormalization group for multilinear disordered Langevin dynamics II: Revisiting the $p=2$ spin dynamics for Wigner and Wishart ensembles
• Scale invariance beyond criticality within the mean-field analysis of tensorial field theories
• Functional renormalization group for p=2 like glassy matrices in the planar approximation: III. Equilibrium dynamics and beyond
• Functional renormalization group for p=2 like glassy matrices in the planar approximation: I. Vertex expansion at equilibrium
• Anomalous higher order Ward identities in tensorial group field theories without closure constraint