Flowing in discrete gravity models and Ward identities: a review

• Published in: European physical journal plus Vol. 136; no. 9; p. 982
• Main Authors: Ousmane Samary, Dine, Lahoche, Vincent, Baloïtcha, Ezinvi
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2021; Springer Nature B.V
• Subjects: Applied and Technical Physics; Atomic; Complex Systems; Condensed Matter Physics; Correlation; Cosmology; Graphs; Gravity; Investigations; Mathematical and Computational Physics; Molecular; Optical and Plasma Physics; Phase transitions; Physics; Physics and Astronomy; Quantum field theory; Quantum gravity; Quantum theory; Review; Spacetime; State-of-the-art reviews; Theoretical
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-021-01823-z

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.