Related papers: Singular topologies in the Boulatov model
We report on some recent results on a class of relativistic lagrangian field theories supporting non-topological soliton solutions and their applications in the contexts of Gravitation and Cosmology. We analyze one and many-components…
Topologically non trivial effects appearing in the discussion of duality transformations in higher genus manifolds are discussed in a simple example, and their relation with the properties of Topological Field Theories is established.
We introduce a linearized version of group field theory. It can be viewed either as a group field theory over the additive group of a vector space or as an asymptotic expansion of any group field theory around the unit group element. We…
We take the first steps in a systematic study of Group Field Theory renormalization, focusing on the Boulatov model for 3D quantum gravity. We define an algorithm for constructing the 2D triangulations that characterize the boundary of the…
In this paper we introduce a unified approach to Toda field theories which allows us to formulate the classes of $A_n$, $B_n$ and $C_n$ models as unique models involving an arbitrary continuous parameter $\nu$. For certain values of $\nu $,…
I review the basic ingredients of discretized gravity which motivate the introduction of Group Field Theory. Thus I describe the GFT formulation of some models and conclude with a few remarks on the emergence of noncommutative structures in…
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…
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…
The aim of this paper is to survey some aspects of mapping class groups with focus on their finite dimensional representations arising in topological quantum field theory.
We investigate various topological spaces and varieties which can be associated to a block of a finite group scheme G. These spaces come from the theory of cohomological support varieties for modules, as well as from the…
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…
Topological conformal field theories are defined using only basic results from the theory of quasiconformal mappings.
We construct a framework which unifyies in dual pairs the fields and anti-fields of the Batalin and Vilkovisky quantization method. We consider gauge theories of p-forms coupled to Yang-Mills fields. Our algorithm generates many topological…
In this work, we generalize several topological results and concepts from ring theory to the setting of monoids.
New constructions in the theory of fields for multiple integrals are designed. Generalizations of the Legendre - Weyl - Caratheodory transforms and corresponding invariant integrals are introduced and explored. Connection and curvature 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 discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to unify certain aspects of the theory of Sobolev inequalities.…
This survey paper concerns mainly with some asymptotic topological properties of finitely presented discrete groups: quasi-simple filtration (QSF), geometric simple connectivity (GSC), topological inverse-representations, and the notion of…
Motivated by potential phenomenological applications, we develop the necessary tools for building GUT models in F-theory. This approach is quite flexible because the local geometrical properties of singularities in F-theory…
We define new topological invariants for Anosov representations and study them in detail for maximal representations of the fundamental group of a closed oriented surface into the symplectic group.