Related papers: Upper Semilattices of Finite-Dimensional Gauges
We study maximal sublattices of finite semidistributive lattices via their complements. We focus on the conjecture that such complements are always intervals, which is known to be true for bounded lattices. Since the class of…
A higher dimensional lattice space can be decomposed into a number of four-dimensional lattices called as layers. The higher dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer…
I discuss a new approach to constructing lattices for gauge theories with extended supersymmetry. The lattice theories themselves respect certain supersymmetries, which in many cases allows the target theory to be obtained in the continuum…
I review motivations for the study of supersymmetric field theories by lattice techniques. In particular, some of the more interesting potential applications are described. These are models of quantum gravity, that rely on the AdS/CFT…
The goal of this paper is to provide some basic structure information on derivations in finite semirings.
The theory of abstract convexity, also known as convexity without linearity, is an extension of the classical convex analysis. There are a number of remarkable results, mostly concerning duality, and some numerical methods, however, this…
Maximal and non-maximal supergravities in three spacetime dimensions allow for a large variety of semisimple and non-semisimple gauge groups, as well as complex gauge groups that have no analog in higher dimensions. In this contribution we…
Various characterizations of finite convex geometries are well known. This note provides similar characterizations for possibly infinite convex geometries whose lattice of closed sets is strongly coatomic and lower continuous. Some classes…
We give a new characterization of pseudoconvex point, and of finite type point, using analytic discs.
We show that every finite semilattice can be represented as an atomized semilattice, an algebraic structure with additional elements (atoms) that extend the semilattice's partial order. Each atom maps to one subdirectly irreducible…
In this work, we present a brief but insightful overview of the gauge theories, which are defined on $ n $-dimensional lattices by using finite gauge groups, in order to show how they can be interpreted as a Hamiltonian system with…
We describe an application of the linear $\de$-expansion to the calculation of correlation functions in SU(2)-Higgs lattice gauge theory. A significant advantage of the technique is that an infinite volume lattice may be used, allowing the…
Crisp and lattice-valued ambiguous representations of one continuous semilattice in another one are introduced and operation of taking pseudo-inverse of the above relations is defined. It is shown that continuous semilattices and their…
In this paper we discuss the notion of completeness of topologized posets and survey some recent results on closedness properties of complete topologized semilattices.
The concept of cutting is first explicitly introduced. By the concept, a convex expansion for finite distributive lattices is considered. Thus, a more general method for drawing the Hasse diagram is given, and the rank generating function…
A comprehensive approach to the theory of higher spin gauge fields is proposed. By explicitly separating out details of implementation from general principles, it becomes possible to focus on the bare minimum of requirements that such a…
This talk is a write-up on some origins of abstract convexity and afew vexing limitations on the range of abstraction in convexity.
We deal with equations over free semilattice of infinite rank and prove that any infinite consistent system of equations is equivalent to its finite subsystem. Moreover, we describe irreducible algebraic sets and solve some algorithmic…
Hypercontractive inequalities are a useful tool in dealing with extremal questions in the geometry of high-dimensional discrete and continuous spaces. In this survey we trace a few connections between different manifestations of…
I review a new treatment of an old idea for light-front quantization of lattice gauge theories and give new results from some illustrative calculations: [I] transverse lattice gauge theory; [II] pure glue; [III] heavy sources and winding…