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Free keywords:
High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
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.
