Functional renormalization group in TGFT - the cyclic-melonic potential approximation

Thürigen, J

Abstract

In tensorial group field theory, continuous spacetime geometry is expected to emerge via phase transition. To understand the theory’s phase diagram we apply the functional renormalization group method. We derive the full flow equation restricting to a cyclic melonic potential and projecting to a constant field in group space. For a tensor field of rank r on U(1) we explicitly calculate beta functions and find equivalence with those of O(N) models but with an effective dimension flowing from r−1 to zero. Thus, fixed points describing a transition between a broken and unbroken phase do not persist and we find universal symmetry restoration.

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