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Towards Renormalizing Group Field Theory

Vincent Rivasseau

Abstract

We review some aspects of non commutative quantum field theory and group field theory, in particular recent progress on the systematic study of the scaling and renormalization properties of group field theory. We thank G. Zoupanos and the organizers of the Corfu 2010 Workshop on Noncommutative Field Theory and Gravity for encouraging us to write this review.

Towards Renormalizing Group Field Theory

Abstract

We review some aspects of non commutative quantum field theory and group field theory, in particular recent progress on the systematic study of the scaling and renormalization properties of group field theory. We thank G. Zoupanos and the organizers of the Corfu 2010 Workshop on Noncommutative Field Theory and Gravity for encouraging us to write this review.

Paper Structure

This paper contains 18 sections, 23 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Scales
  3. The Grosse-Wulkenhaar model
  4. The new scale decomposition
  5. The Moyality principle
  6. Noncommutative Renormalization
  7. Group Field Theory
  8. GFT as theories of Holonomies
  9. $2D$ GFT as Matrix Models
  10. General Relativity in three dimensions
  11. Group Field Theory in three dimensions
  12. The 4 Dimensional Case
  13. 4D GFT Vertex
  14. The EPR/FK theory
  15. Renormalization group, at last?
  16. ...and 3 more sections

Figures (3)

  • Figure 1: The Moyal vertex
  • Figure 2: The Moyality principle
  • Figure 3: The pentachore

Theorems & Definitions (2)

  • Definition 1
  • Definition 2