# The tensor theory space

@article{Rivasseau2014TheTT, title={The tensor theory space}, author={V. Rivasseau}, journal={Fortschritte der Physik}, year={2014}, volume={62} }

The tensor track is a background‐independent discretization of quantum gravity which includes a sum over all topologies. We discuss how to define a functional renormalization group flow and the Wetterich equation in the corresponding theory space. This space is different from the Einsteinian theory space of asymptotic safety. It includes all fixed‐rank tensor‐invariant interactions, hence generalizes matrix models and the (Moyal) non‐commutative field theory space.

## 39 Citations

### Random Tensors and Quantum Gravity

- Physics
- 2016

We provide an informal introduction to tensor field theories and to their as- sociated renormalization group. We focus more on the general motivations coming from quantum gravity than on the…

### Constructive Tensor Field Theory: the T 4 3 Model

- Mathematics
- 2016

: We build constructively the simplest tensor ﬁeld theory which requires some renormalization, namely the rank three tensor theory with quartic interactions and propagator inverse of the Laplacian on…

### Renormalization and Hopf algebraic structure of the five-dimensional quartic tensor field theory

- Mathematics
- 2015

This paper is devoted to the study of renormalization of the quartic melonic tensor model in dimension (=rank) five. We review the perturbative renormalization and the computation of the one loop…

### Renormalization of a tensorial field theory on the homogeneous space SU(2)/U(1)

- Physics
- 2015

We study the renormalization of a general field theory on the homogeneous space (SU(2)/ U(1))×d with tensorial interaction and gauge invariance under the diagonal action of SU(2). We derive the power…

### The Tensor Track, IV

- Computer Science
- 2016

These developments center around understanding the interface between random matrices and random tensors through the intermediate field representation, finding new types of 1/N expansions by enhancing sub-leading tensor interactions, exploring the renormalization group flows in the tensor theory space, and developing the constructive aspects of the theory.

### A Renormalizable SYK-Type Tensor Field Theory

- PhysicsAnnales Henri Poincaré
- 2018

In this paper we introduce a simple field theoretic version of the Carrozza–Tanasa–Klebanov–Tarnopolsky (CTKT) “uncolored” holographic tensor model. It gives a more familiar interpretation to the…

### A Renormalizable SYK-Type Tensor Field Theory

- PhysicsAnnales Henri Poincaré
- 2018

In this paper we introduce a simple field theoretic version of the Carrozza–Tanasa–Klebanov–Tarnopolsky (CTKT) “uncolored” holographic tensor model. It gives a more familiar interpretation to the…

### Renormalization of an Abelian tensor group field theory: solution at leading order

- Mathematics, Physics
- 2015

A bstractWe study a just-renormalizable tensorial group field theory of rank six with quartic melonic interactions and Abelian group U(1). We introduce the formalism of the intermediate field, which…

### Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term sum_s|p_s| + \mu

- Mathematics
- 2015

We consider the parametric representation of the amplitudes of Abelian models in the so-called framework of rank d Tensorial Group Field Theory. These models are called Abelian because their elds…

### Flowing in discrete gravity models and Ward identities: a review

- PhysicsThe European Physical Journal Plus
- 2021

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

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We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for…