Monopoles and Coulomb Gas Representation of the QCD Effective Lagrangian
Abstract
A novel Coulomb gas (CG) description of low energy QCD4(Nc) is constructed. The construction is based on the dual transformation of the QCD effective Lagrangian. By considering a large gauge transformation, the charges of this statistical system are identified with magnetic monopoles which carry fractional charges of strength 1/Nc. Furthermore, the creation operator which inserts the magnetic charge in the CG picture is explicitly constructed and demonstrated to have a non-zero vacuum expectation value, indicating that confinement does occur. The Wilson loop operator as well as the creation operator for the domain wall in CG representation is also constructed. Additional support for the D-brane picture suggested by Witten is also found. Lastly, the relation of the CG picture with the instanton-quarks is also discussed.
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