Recent results on topology on the lattice (in memory of Pierre van Baal)

Topological clusters in SU(2) gluodynamics at finite temperature and the evidence for KvB calorons

We report on our search for Kraan-van Baal calorons in finite temperature SU(2) lattice ensembles. We also discuss recent progress made in developing a caloron-anticaloron gas model decribing confinement and deconfinement in the context of trivial and non-trivial holonomy.

Gauge topology and confinement: an update

In the instanton ensemble the fermionic zero modes collectivize and break chiral symmetry. Recent studies of resulting zero mode zone confirm its very small width and overall importance for lattice simulations. Confinement however has been related with completely different topological objects, the magnetic monopoles. Instanton constituents -- instanton dyons, discovered at nonzero holonomy by Pierre van Baal and others -- are able to explain both confinement and chiral symmetry breaking. The talk summarizes recent works deriving the instanton-dyon mutual interactions, and statistical studies o…

Searching for KvBLL calorons in SU(3) lattice gauge field ensembles

We discuss Kraan - van Baal - Lee - Lu (KvBLL) solutions of the classical Yang-Mills equations with temperature in the context of SU(3) lattice gauge theory. We present discretized lattice versions of KvBLL solutions and other dyonic structures, obtained by cooling in order to understand their variety and signature. An analysis of the zero modes of the lattice Dirac operator for different fermionic boundary conditions gives clear evidence for a KvBLL-like background of finite T lattice subensembles with Q = +/-1. Using APE-smearing we are able to study the topological charge density q(x) of th…

关于 $SU(N)/\mathbb{Z}_N$ 规范理论中广义对称性的格点描述的注记

Note on lattice description of generalized symmetries in $SU(N)/\mathbb{Z}_N$ gauge theories

本文基于广义 Lüscher 格点拓扑构造，用松弛上闭链的 $SU(N)$ 格点规范场描述 $SU(N)/\mathbb{Z}_N$ 主丛、分数拓扑荷及中心1-形式对称性，并与 Kapustin–Seiberg 方案等价。