Ward identity violation for melonic $T^4$-truncation

Understand

Referring to recent works concerning the functional renormalization group for tensorial group fields theories [arXiv:1803.09902] and [arXiv:1809.00247], this paper gives in-depth explanation for, the ambiguity around the search of fixed points in the Wetterich flow equation and the Ward-Takahashi identities.

• We consider the $U(1)$-tensors models and discuss the non-existence of phase transition taking into account the Ward-identities as new constraint along the flow.
• We prove that the quartic melonic tensorial group fields theories without closure constraint are devoid with the fixed points and therefore the phase transitions.