Gauge and scalar fields on : A gauge-invariant analysis. II. The measure for gauge fields and a 4d WZW theory
Dimitra Karabali (Physics and Astronomy Department, Lehman College, CUNY, Bronx, New York 10468, USA, The Graduate Center, CUNY, New York, New York 10016, USA); Antonina Maj (Physics and Astronomy Department, Lehman College, CUNY, Bronx, New York 10468, USA, The Graduate Center, CUNY, New York, New York 10016, USA, Physics Department, City College of New York, CUNY, New York, New York 10031, USA); V. P. Nair (The Graduate Center, CUNY, New York, New York 10016, USA, Physics Department, City College of New York, CUNY, New York, New York 10031, USA)
We consider the volume of the gauge orbit space for gauge fields on four-dimensional complex projective space. The analysis uses a parametrization of gauge fields where gauge transformations act homogeneously on the fields, facilitating a manifestly gauge-invariant analysis. The volume element contains a four-dimensional Wess-Zumino-Witten (WZW) action for a Hermitian matrix-valued field. There is also a masslike term for certain components of the gauge field. We discuss how the mass term could be related to results from lattice simulations as well as Schwinger-Dyson equations. We argue for a kinematic regime where the Yang-Mills theory can be approximated by the 4d-WZW theory. The result is suggestive of the instanton liquid picture of QCD. Further it is also indicative of the mechanism for confinement being similar to what happens in two dimensions.
