Related papers: Group field theory on 2-groups

Group field theories are particular quantum field theories defined on D copies of a group which reproduce spin foam amplitudes on a space-time of dimension D. In these lecture notes, we present the general construction of group field…

Group field theories are a generalization of matrix models which provide both a second quantized reformulation of loop quantum gravity as well as generating functions for spin foam models. While states in canonical loop quantum gravity, in…

Group field theories are higher dimensional generalizations of matrix models. Their Feynman graphs are fat and in addition to vertices, edges and faces, they also contain higher dimensional cells, called bubbles. In this paper, we propose a…

Group Field Theories (GFT) are quantum field theories over group manifolds; they can be seen as a generalization of matrix models. GFT Feynman graphs are tensor graphs generalizing ribbon graphs (or combinatorial maps); these graphs are…

Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs…

A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible…

We present a new group field theory model, generalising the Boulatov model, which incorporates both 3-dimensional gravity and matter coupled to gravity. We show that the Feynman diagram amplitudes of this model are given by Riemannian…

We give a very brief introduction to the group field theory approach to quantum gravity, a generalisation of matrix models for 2-dimensional quantum gravity to higher dimension, that has emerged recently from research in spin foam models.

Group field theories are a new type of field theories over group manifolds and a generalization of matrix models, that have recently attracted much interest in quantum gravity research. They represent a development of and a possible link…

Group Field Theories, a generalization of matrix models for 2d gravity, represent a 2nd quantization of both loop quantum gravity and simplicial quantum gravity. In this paper, we construct a new class of Group Field Theory models, for any…

Group field theory is a background-independent approach to quantum gravity whose starting point is the definition of a quantum field theory on an auxiliary group manifold (not interpreted as spacetime, but rather as the finite-dimensional…

We give a brief overview of the properties of a higher dimensional generalization of matrix model which arises naturally in the context of a background independent approach to quantum gravity, the so called group field theory. We show that…

We present a new Group Field Theory for 4d quantum gravity. It incorporates the constraints that give gravity from BF theory, and has quantum amplitudes with the explicit form of simplicial path integrals for 1st order gravity. The…

This thesis provides an introduction to the various category theory ideas employed in topological quantum field theory. These theories are viewed as symmetric monoidal functors from topological cobordism categories into the category of…

Just as 3d state sum models, including 3d quantum gravity, can be built using categories of group representations, "2-categories of 2-group representations" may provide interesting state sum models for 4d quantum topology, if not quantum…

Gauge theories admit a generalisation in which the gauge group is replaced by a finer algebraic structure, known as a 2-group. The first model of this type is a Topological Quantum Field Theory introduced by Yetter. We discuss a common…

In the context of quantum gravity, group field theories are field theories that generate spinfoam amplitudes as Feynman diagrams. They can be understood as generalizations of the matrix models used for 2d quantum gravity. In particular…

A generalization of the matrix model idea to quantum gravity in three and higher dimensions is known as group field theory (GFT). In this paper we study generalized GFT models that can be used to describe 3D quantum gravity coupled to point…

Group field theories (GFT) are higher dimensional generalizations of matrix models whose Feynman diagrams are dual to triangulations. Here we propose a modification of GFT models that includes extra field indices keeping track of the…

We construct a group field theory model for quantum gravity minimally coupled to relativistic scalar fields, defining as well a corresponding discrete gravity path integral (and, implicitly, a coupled spin foam model) in its Feynman…