SU(N) reduced, quenched, gauge theories have been shown to be related to string theories. We extend this result and show how a 4-dimensional, reduced, quenched, Yang–Mills theory, supplemented by the topological term, can be related through the Wigner–Weyl–Moyal correspondence to an open 3-brane model. The boundary of the 3-brane is described by a Chern–Simons 2-brane. We identify the bulk of the 3-brane with the interior of a hadronic bag and the world-volume of the Chern–Simons 2-brane with the dynamical boundary of the bag. We estimate the value of the induced bag constant to be a little less than 200 MeV.
