Related papers: Two-dimensional algebra in lattice gauge theory
Previous work in the literature has studied the Hamiltonian structure of an R-squared model of gravity with torsion in a closed Friedmann-Robertson-Walker universe. Within the framework of Dirac's theory, torsion is found to lead to a…
We explore various aspects of 2-form topological gauge theories in (3+1)d. These theories can be constructed as sigma models with target space the second classifying space $B^2G$ of the symmetry group $G$, and they are classified by…
The low-energy behavior of near-extremal black holes can be understood from the near-horizon AdS_2 region. In turn, this region is effectively described by using Jackiw-Teitelboim gravity coupled to Yang-Mills theory through the…
In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…
String diagrams are a graphical language used to represent processes that can be composed sequentially or in parallel, which correspond graphically to horizontal or vertical juxtaposition. In this paper we demonstrate how to compute the…
We apply a recent duality theorem for tangles in abstract separation systems to derive tangle-type duality theorems for width-parameters in graphs and matroids. We further derive a duality theorem for the existence of clusters in large data…
Network theory has proven to be a powerful tool in describing and analyzing systems by modelling the relations between their constituent objects. In recent years great progress has been made by augmenting `traditional' network theory.…
We show that the transition laws for a 2-connection can be recovered by discretizing the base 2-space of a 2-bundle into an Euclidean hypercubic lattice. The aim of this work is to serve as an example of how important results in higher…
Motivated by team semantics and existential second-order logic, we develop a model-theoretic framework for studying second-order objects such as sets and relations. We introduce a notion of abstract elementary team categories that…
A gauge invariant Hamiltonian representation for SU(2) in terms of a spin network basis is introduced. The vectors of the spin network basis are independent and the electric part of the Hamiltonian is diagonal in this representation. The…
We present an action for a six-dimensional superconformal field theory containing a non-abelian tensor multiplet. All of the ingredients of this action have been available in the literature. We bring these pieces together by choosing the…
Parallel transport is an important step in many discrete algorithms for statistical computing on manifolds. Numerical methods based on Jacobi fields or geodesics parallelograms are currently used in geometric data processing. In this last…
We show that standard identities and theorems for lattice models with $U(1)$ symmetry get re-expressed discretely in the tensorial formulation of these models. We explain the geometrical analogy between the continuous lattice equations of…
For a smooth manifold $M$, possibly with boundary and corners, and a Lie group $G$, we consider a suitable description of gauge fields in terms of parallel transport, as groupoid homomorphisms from a certain path groupoid in $M$ to $G$.…
In this article we define and investigate a notion of parallel transport on finite projective modules over finite matrix algebras. Given a derivation-based differential calculus on the algebra and a connection on the module, we construct…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
We discuss how to formulate lattice gauge theories in the Tensor Network language. In this way we obtain both a consistent truncation scheme of the Kogut-Susskind lattice gauge theories and a Tensor Network variational ansatz for gauge…
Interactions and relations between objects may be pairwise or higher-order in nature, and so network-valued data are ubiquitous in the real world. The "space of networks", however, has a complex structure that cannot be adequately described…
We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…
For any cluster algebra whose underlying combinatorial data can be encoded by a bordered surface with marked points, we construct a geometric realization in terms of suitable decorated Teichmueller space of the surface. On the geometric…