Flowing in discrete gravity models and Ward identities: a review

Ezinvi Baloitcha , Vincent Lahoche (1) , Dine Ousmane Samary (1)

1 LIST (CEA) - Laboratoire d'Intégration des Systèmes et des Technologies

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. We attached great importance to the pedagogy and the self-consistency of the presentation.

Mots clés: Tensorial group field theories; Matrix models; large-N limit; Ward-Takahashi identities; renormalization group; quantum gravity; model: discrete; renormalization group: nonperturbative; field theory: statistical; gravitation: discrete; field theory: group; gravitation: model; Ward-Takahashi identity; field theory; conservation law; Ward identity; matrix model; reflection; Noether

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Ezinvi Baloitcha, Vincent Lahoche, Dine Ousmane Samary. Flowing in discrete gravity models and Ward identities: a review. Eur.Phys.J.Plus, 2021, 136 (9), pp.982. ⟨10.1140/epjp/s13360-021-01823-z⟩. ⟨hal-02458725⟩