Functional renormalisation group approach for tensorial group field theory: a rank-3 model

Benedetti, Dario (Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Mühlenberg 1, Potsdam, 14476, Germany) ; Geloun, Joseph (Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Mühlenberg 1, Potsdam, 14476, Germany) (International Chair in Mathematical Physics and Applications, ICMPA-UNESCO Chair, University of Abomey-Calavi, Cotonou, Benin) ; Oriti, Daniele (Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Mühlenberg 1, Potsdam, 14476, Germany)

19 March 2015

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) 3 , endowed with a kinetic term linear in the momenta and with 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. 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.


Published in: JHEP 1503 (2015) 084
Published by: Springer/SISSA
DOI: 10.1007/JHEP03(2015)084
arXiv: 1411.3180
License: CC-BY-4.0



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