Related papers: Group field theory on 2-groups
We construct a topological field theory which, on the one hand, generalizes BF theories in that there is non-trivial coupling to `topological matter fields'; and, on the other, generalizes the three-dimensional model of Carlip and Gegenberg…
Outlined in this paper is a description of \emph{equivariance} in the world of 2-dimensional extended topological quantum field theories, under a topological action of compactLie groups. In physics language, I am gauging the theories ---…
This article surveys the application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems. The common thread in the discussion is the construction of quantum fields using…
In this short review we introduce group field theory, a particular class of random tensor models, which represents nowadays one of the candidates for a fundamental theory of quantum gravity. We insist on the combinatorial richness of…
It was recently argued that quantum field theories possess one-form and higher-form symmetries, labelled `generalized global symmetries.' In this paper, we describe how those higher-form symmetries can be understood mathematically as…
We show that the equations of motion defined over a specific field space are realizable as operator conditions in the physical sector of a generalized Floer theory defined over that field space. The ghosts associated with such a…
Spin foam models, loop quantum gravity and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravity inspired models with finite groups,…
Tensor models and, more generally, group field theories are candidates for higher-dimensional quantum gravity, just as matrix models are in the 2d setting. With the recent advent of a 1/N-expansion for coloured tensor models, more focus has…
Group field theories have recently been shown to admit a 1/N expansion dominated by so-called `melonic graphs', dual to triangulated spheres. In this note, we deepen the analysis of this melonic sector. We obtain a combinatorial formula for…
We present a precise definition of extended homotopy quantum field theories and develop an orbifold construction for these theories when the target space is the classifying space of a finite group $G$, i.e. for $G$-equivariant topological…
Extending tensor models at the field theoretical level, tensor field theories are nonlocal quantum field theories with Feynman graphs identified with simplicial complexes. They become relevant for addressing quantum topology and geometry in…
We study a topological field theory describing confining phases of gauge theories in four dimensions. It can be formulated on a lattice using a discrete 2-form field talking values in a finite abelian group (the magnetic gauge group). We…
This paper reviews the construction of quantum field theory on a 4-dimensional spacetime by combinatorial methods, and discusses the recent developments in the direction of a combinatorial construction of quantum gravity.
We present a topological quantum field theory which corresponds to the moduli problem associated to Witten's monopole equations for four-manifolds. The construction of the theory is carried out in purely geometrical terms using the…
The theory of Poisson-$\sigma$-models employs the mathematical notion of Poisson manifolds to formulate and analyze a large class of topological and almost topological two dimensional field theories. As special examples this class of field…
This thesis is broadly split into two parts. In the first part, simple state sum models for minimally coupled fermion and scalar fields are constructed on a $1$-manifold. The models are independent of the triangulation and give the same…
We describe the doubled space of Double Field Theory as a group manifold $G$ with an arbitrary generalized metric. Local information from the latter is not relevant to our discussion and so $G$ only captures the topology of the doubled…
We offer a perspective on some recent results obtained in the context of the group field theory approach to quantum gravity, on top of reviewing them briefly. These concern a natural mechanism for the emergence of non-commutative field…
We study the quantum mechanics of a system of topologically interacting particles in 2+1 dimensions, which is described by coupling the particles to a Chern-Simons gauge field of an inhomogeneous group. Analysis of the phase space shows…
We construct a generalised formalism for group field theories, in which the domain of the field is extended to include additional proper time variables, as well as their conjugate mass variables. This formalism allows for different types of…