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Chiral Quark Dynamics and the Ramond-Ramond U(1) Gauge Field

Topological excitations in the QCD vacuum take the form of coherent codimension one sheets with positive and negative sheets juxtaposed in a dipole layer. These sheets may be interpreted as Luscher's "Wilson bags," which are domain walls between discrete quasivacua labelled by a local value of the $θ$ parameter equal to $2πk$, with $k$ given by the number of units of background Ramond-Ramond flux. This picture of the vacuum is closely analogous to Coleman's description of the 2D massive Schwinger model, where $θ$ is interpreted as a background electric field, and a pointlike charged particle is a domain wall between vacua which differ by one unit of background electric flux. The main effect of the Ramond-Ramond U(1) field in low energy QCD dynamics is the generation of phenomenologically important contact terms: (1) The dominant contact term in the topological charge correlator which leads to positive topological susceptibility, (2) The $η'$ mass insertion, and (3) An $SU(N_f)\times SU(N_f)$ invariant Nambu-Jona Lasinio 4-quark interaction.