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In nuclear physics, the chiral model is a phenemological model describing mesons in the chiral limit where the masses of the quarks goes to zero (without mentioning quarks at all). It's a nonlinear sigma model with the principal homogeneous space of the Lie group SU(N) as its target manifold where N is the number of quark flavors. The Riemannian metric of the target manifold is given by a positive constant multiplied by the Killing form acting upon the Maurer-Cartan form of SU(N). The internal global symmetry of this model is SU(N)L×SU(N)R, the left and right copies respectively where the left copy acts as the left action upon the target space and the right copy acts as the right action. The left copy describes rotations among the left-handed quarks while the right copy describes rotations among the right-handed quarks and they are independent of each other. This model admits topological solitons called Skyrmions.
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