Chern-Simons Hadronic Bag from Quenched Large-$N$ QCD

S. Ansoldi¹

Dipartimento di Fisica Teorica dell'Università,

Istituto Nazionale di Fisica Nucleare, Sezione di Trieste,

Strada Costiera 11, 34014-Trieste, Italy

C. Castro²

Center for Theoretical Studies of Physical Systems

Clark Atlanta University, Atlanta, GA30314

E.Spallucci³

Dipartimento di Fisica Teorica dell'Università,

Istituto Nazionale di Fisica Nucleare, Sezione di Trieste,

Strada Costiera 11, 34014-Trieste, Italy

Abstract:

$SU(N)$ 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 an hadronic bag, and the Chern-Simons $2$-brane with dynamical boundary of the bag. We estimate the value of the induced bag constant to be a little less than $200\,\mathrm{MeV}$.