Large Nc Limit Baryon Emergent Symmetry Research Based On Lie Group Induced Representation Theory

In this paper we mainly investigate the emergent symmetry,the contracted SU(8) group which is obtained in the large Nc limit of the Quantum Chromodynamics.We analyze the algebra structure of this emergent symmetry group and construct all the irreducible representations by the method of induced representation theory.We obtain the Exotic Baryon multiplets from the induced representation using the project operator.In the Standard Model of particle physics,the non-relativistic quarks have the symmetry of SU(2)_spin(?)SU(N_F)_flavor(?)SU(3)_color.The color SU(3)_coloris a dynamic symmetry,which can be localized to introduce gauge interaction.This gauge interaction is the gauge field propagates the strong interaction,which is the so called Quantum Chromodynamics(QCD).At the low energy scales,one can not apply a perturbative expansion to QCD because of the infrared-forbidden mechanism.So,we need to develop phenomenological low energy effective theory to understanding the experimental results. The large Nc expansion is a useful low energy effective theory,which is introduced in the physical model concerning the banded states such as mesons and baryons.After taking the large Nc QCD effect into account,there is an emergent symmetry,the so called contracted group SU(2N_F)_contracted:SU(2)_spin(?)SU(N_F)_flavor×A,where A is Abelian.And the emergent symmetry group is the semi-direct product of the non-Abelian group SU(2)_spin(?)SU(N_F)_flavorand the Abelian group A.It is very important to investigate the unitary irreducible representations of this emergent group for understanding the large Nc QCD phenomena such as the exotic baryons.In this paper we mainly study the emergent symmetry of the Baryon in the large Nc limit by the induced representation theory.We discuss in great detail the contracted SU(8) group in the case of the flavor number F=4.We analyze the semi-direct product group structure of the contracted SU(8)group.We classify the orbits and obtain the corresponding little group for each orbit.We construct the irreducible representations for this dynamical system by the induced representation theory.By the Euler angle parameterization of SU(4)group using a pictorial method,we separate the SU(4)into cosets respect to the little group,and the explicit coset representive elements are obtained in Euler angle parameters.We discuss the induced representation constrained on the spin and flavor SU(2)_spin(?)SU(4)_flavorsymmetry group of the system.By the project operator, we can separate the particular irreducible representation of the SU(2)_spin(?)SU(4)_flavor group from the induced representation,and obtain the corresponding Baryon multiplets. In the end of the paper we analyze these multiplets with Young diagram technique and some multiplets which contain the exotic Baryon states are point out.