Vacuum Structure of 2+1-Dimensional Gauge Theories

Tom 39 / 1997

Manuel Asorey, Fernando Falceto, Jose Lopez, Gloria Luzon Banach Center Publications 39 (1997), 183-199 DOI: 10.4064/-39-1-183-199


We analyse some non-perturbative properties of the Yang-Mills vacuum in two-dimensional spaces in the presence of Chern-Simons interactions. We show that the vacuum functional vanishes for some gauge field configurations. We have identified some of those nodal configurations which are characterized by the property of carrying a non-trivial magnetic charge. In abelian gauge theories this fact explains why magnetic monopoles are suppressed by Chern-Simons interactions. In non-abelian theories it suggests a relevant role for nodal gauge field configurations in the confinement mechanism of Yang-Mills theories. In topological Chern-Simons theories nodal configurations belong to Atiyah-Bott strata with non-null codimension in the space of gauge field configurations. In the presence of external static quarks some nodes of the vacuum functional with non-trivial magnetic charge are removed and they are responsible for the increase of vacuum energy.


  • Manuel Asorey
  • Fernando Falceto
  • Jose Lopez
  • Gloria Luzon

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