Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
Year: 2015
Type: article
Abstract: We set up the Functional Renormalisation Group formalism for Tensorial Group Field Theory in full generality. We then apply it to a rank-3 model over U(1) x U(1) x U(1), endowed with a linear kinetic term and nonlocal interactions. The system of FRG equations turns out to be non-autonomous in the RG flow parameter. This feature is explained by the existence of a hidden scale, the radius of the group manifold. We investigate in detail the opposite regimes of large cut-off (UV) and small cut-off (IR) of the FRG equations, where the system becomes autonomous, and we find, in both case, Gaussian and non-Gaussian fixed points. We derive and interpret the critical exponents and flow diagrams associated with these fixed points, and discuss how the UV and IR regimes are matched at finite N. Finally, we discuss the evidence for a phase transition from a symmetric phase to a broken or condensed phase, from an RG perspective, finding that this seems to exist only in the approximate regime of very large radius of the group manifold, as to be expected for systems on compact manifolds.
Source: Max Planck Digital Library
Authors: Benedetti, D., Geloun, J., Oriti, D.
Institution: Max Planck Institute for Gravitational Physics
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3101097204