Topological Objects and Confinement in Non-Abelian Lattice Gauge Theory

We use lattice methods to study the connection between topological objects and the confining potential in SU(2) and SU(3) Yang-Mills theories. We use Monte Carlo techniques, generating and performing measurements on sample configurations of SU(2) and SU(3) gauge fields. We isolate topological objects, specifically Abelian monopoles and center vortices, in these configurations. We then measure the contribution to the string tension from these objects, and compare the results to “full” measurements made on the original configurations. In addition we investigate the effects of gauge ambiguities (Gribov effects) and cooling on these sets of measurements. For the case of SU(2) lattice gauge theory, our results from monopoles agree with full values but are somewhat lower when gauge ambiguities are taken into account. The situation is not stable under cooling. When we carry out analogous procedures on sample SU(3) lattice configurations, we find disagreement between full SU(3) values and those from topological objects, with our results from topological objects being lower than the full SU(3) values. This disagreement becomes more substantial after the effects of gauge ambiguities are taken into account. We conclude that present methods for identifying and extracting topological objects are inadequate for explaining confinement in the realistic case of an SU(3) gauge group.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Year dc:date

2012

Author dc:creator

• Tucker, William Walden

• Topological
• abelian
• Lattice Gauge
• monopoles
• yang-mills
• monte carlo
• asymbiotic
• quenched approximations
• quark
• antiquark
• quark-antiquark
• wilson loop
• nielson-olesen
• homotopy
• invariants
• polyakov
• dirac
• superconductor
• gribov effect
• submanifold
• magnetic currents
• overrelaxation

Statement dc:rights

• 2005 Tucker ©

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/35262

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/35262