Flowing in discrete gravity models and Ward identities: A review

Understand

Ward-Takahashi identities are nonperturbative relations between correlation functions and arising from symmetries in quantum and statistical fields theories, as Noether currents conservation for classical theories.

• Since their historical origin, these identities were considered to prove the exact relation between counter-terms to all order of the perturbative expansion.
• Recently they have been considered in relation with nonperturbative renormalization group aspects for some classes of quantum field theories namely tensorial group field theories and matrix models, both characterized by a specific non-locality in their interactions, and expected to provide discrete models for quantum gravity.
• In this review, we summarize the state of the art, focusing on the conceptual aspects rather than technical subtleties, and provide a unified reflection on this novel and promising way of investigation.