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

TL;DR

This paper investigates the impact of Ward identity violations on the fixed points and phase transitions in melonic tensorial group field theories, revealing their non-existence under certain conditions.

Contribution

It provides a detailed analysis of Ward identity violations in $T^4$-truncation models, demonstrating the absence of fixed points and phase transitions in unclosed melonic tensorial group field theories.

Findings

No fixed points in unclosed melonic tensorial models

Ward identities constrain the flow, preventing phase transitions

Clarifies ambiguities in the functional renormalization group analysis

Abstract

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.