Topological objects in QCD

Abstract

Topological excitations are prominent candidates for explaining nonperturbative effects in QCD like confinement. In these lectures, I cover both formal treatments and applications of topological objects. The typical phenomena like BPS bounds, topology, the semiclassical approximation and chiral fermions are introduced by virtue of kinks. Then I proceed in higher dimensions with magnetic monopoles and instantons and special emphasis on calorons. Analytical aspects are discussed and an overview over models based on these objects as well as lattice results is given.

28 pages, 17 figures; Lectures given at 45th Internationale Universitaetswochen fuer Theoretische Physik (International University School of Theoretical Physics): Conceptual and Numerical Challenges in Femto- and Peta-Scale Physics, Schladming, Styria, Austria, 24 Feb - 3 Mar 2007

References in corpus (6)

• Linking confinement to spectral properties of the Dirac operator
• Exploring the structure of the quenched QCD vacuum with overlap fermions
• Spectral sums of the Dirac-Wilson Operator and their relation to the Polyakov loop
• An SU(2) KvBLL caloron gas model and confinement
• Complete spectra of the Dirac operator and their relation to confinement
• Localization properties of fermions and bosons

Cited by in corpus (13)

• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• QCD-like Theories on R_3\times S_1: a Smooth Journey from Small to Large r(S_1) with Double-Trace Deformations
• Instanton constituents in the O(3) model at finite temperature
• Instanton constituents and fermionic zero modes in twisted CP(n) models
• Fermionic boundary conditions and the finite temperature transition of QCD
• Intersections of thick Center Vortices, Dirac Eigenmodes and Fractional Topological Charge in SU(2) Lattice Gauge Theory
• Chiral Symmetry Breaking on the Lattice
• Cautionary remarks on the moduli space metric for multi-dyon simulations
• The Vortex Structure of SU(2) Calorons
• Thermodynamics of the O(3) model in 1+1 dimensions: lattice vs. analytical results
• Building imaginary-time thermal field theory with artificial neural networks
• Vacuum structure and string tension in Yang-Mills dimeron ensembles
• Emergent Kink Statistics at Finite Temperature