Related papers: Surgery in colored tensor models

We use a mix of field theoretic and holographic techniques to elucidate various properties of quantum entanglement entropy. In (3+1)-dimensional conformal field theory we study the divergent terms in the entropy when the entangling surface…

Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…

We give diagrammatic algorithms for computing the group trisection, homology groups, and intersection form of a closed, orientable, smooth 4-manifold, presented as a branched cover of a bridge-trisected surface in $\mathbb{S}^{4}$. The…

In this paper, we introduce the concept of 3-alterfolds with embedded separating surfaces. When the separating surface is decorated by a spherical fusion category, we obtain quantum invariants of 3-alterfold, which is consistent with many…

Colored tensor models generalize matrix models in arbitrary dimensions yielding a statistical theory of random higher dimensional topological spaces. They admit a 1/N expansion dominated by graphs of spherical topology. The simplest tensor…

We present new numerical results on the space of local, unitary, parity-preserving conformal field theories (CFTs) in three dimensions from the stress tensor bootstrap. In bounds maximizing certain OPE coefficients, we find a plethora of…

The Chern-Simons (CS) theory in three dimensions with a compact gauge group G is studied. Starting from the BRST quantization of the theory defined in R^3, the values of gauge invariants observables are computed in any closed and orientable…

Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual foundations for this canvas, and how these can…

Topological surgery occurs in natural phenomena where two points are selected and attracting or repelling forces are applied. The two points are connected via an invisible `thread'. In order to model topologically such phenomena we…

In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…

In this paper, we provide two different resolutions of structural sheaves of projectivized tangent bundles of smooth complete intersections. These resolutions allow in particular to obtain convenient (and completely explicit) descriptions…

In this paper we introduce a technique, called rim surgery, which can change a smooth embedding of an orientable surface of positive genus and nonnegative self-intersection in a smooth 4-manifold while leaving the topological embedding…

We describe how a spin-foam state sum model can be reformulated as a quantum field theory of spin networks, such that the Feynman diagrams of that field theory are the spin-foam amplitudes. In the case of open spin networks, we obtain a new…

We use topological surgery in dimension four to give sufficient conditions for the zero framed surgery manifold of a 3-component link to be homology cobordant to the 3-torus, which arises from zero framed surgery on the Borromean rings, via…

We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.

We present three large families of new examples of plumbed 3-manifolds that bound rational homology 4-balls. These are constructed using two operations, also defined here, that preserve the lack of a lattice embedding obstruction to…

A background-independent route towards a universal continuum limit in discrete models of quantum gravity proceeds through a background-independent form of coarse graining. This review provides a pedagogical introduction to the conceptual…

We investigate the construction of coherent states for quantum theories of connections based on graphs embedded in a spatial manifold, as in loop quantum gravity. We discuss the many subtleties of the construction, mainly related to the…

A 3-dimensional topological quantum field theory (TQFT) is a symmetric monoidal functor from the category of 3-cobordisms to the category of vector spaces. Such TQFTs provide in particular numerical invariants of closed 3-manifolds such as…

A model of simplicial quantum gravity in three dimensions is investigated numerically based on the technique of the dynamical triangulation (DT). We are concerned with the surfaces appearing on boundaries (i.e., sections) of…