The Tensor Theory Space

Abstract

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.

This short note is intended as a complement to arXiv:1311.1461, to appear in the Proceedings of the Workshop on Noncommutative Field Theory and Gravity in Corfu September 2013, Fortshritt. Phys. 2014

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Cited by in corpus (28)

• Functional Renormalisation Group Approach for Tensorial Group Field Theory: a Rank-3 Model
• Invitation to Random Tensors
• Functional Renormalisation Group analysis of Tensorial Group Field Theories on ${\mathbb{R}}^d$
• Asymptotic safety in three-dimensional SU(2) Group Field Theory: evidence in the local potential approximation
• Correlation functions of just renormalizable tensorial group field theory: The melonic approximation
• Towards phase transitions between discrete and continuum quantum spacetime from the Renormalization Group
• Renormalization of an Abelian Tensor Group Field Theory: Solution at Leading Order
• Random Tensors and Quantum Gravity
• Nonperturbative renormalization group beyond melonic sector: The Effective Vertex Expansion method for group fields theories
• Functional renormalization group for the $U(1)$-$T_5^6$ tensorial group field theory with closure constraint
• Constructive tensor field theory: The $T_4^4$ model
• Constructive Tensor Field Theory: The $T_3^4$ Model
• Ward identity violation for melonic $T^4$-truncation
• Progress in the solving nonperturbative renormalization group for tensorial group field theory
• Unitary symmetry constraints on tensorial group field theory renormalization group flow
• Parametric Representation of Rank d Tensorial Group Field Theory: Abelian Models with Kinetic Term ${\sum }_s|p_s|+\mu$
• Reliability of the local truncations for the random tensor models renormalization group flow
• Flowing in discrete gravity models and Ward identities: A review
• Tullio Regge's legacy: Regge calculus and discrete gravity
• Renormalization group flow of coupled tensorial group field theories: Towards the Ising model on random lattices
• Renormalization and Hopf Algebraic Structure of the 5-Dimensional Quartic Tensor Field Theory
• Surgery in colored tensor models
• Nontrivial UV behavior of rank-4 tensor field models for quantum gravity
• A Renormalizable SYK-type Tensor Field Theory
• No Ward-Takahashi identity violation for an Abelian tensorial group field theories with closure constraint
• A power counting theorem for a $p^{2a}{\varphi }^4$ tensorial group field theory
• New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and Applications
• Melonic large $N$ limit of $5$-index irreducible random tensors