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hi!
in the first page of the attached pdf, after the title " 't hooft double line notation", he says that we have to consider the gluon as NxN traceless hermitian matrices to convince ourselves about the double line notation.
there is my question: if you want the indices a,b to run from 1 to N, you need the T^A generators to be NxN matrices, and that means that you are in the fundamental representation, right?
but when you look for a demonstration of the 't hooft's planar limit, it seems that you need the gauge bosons to be in the adjoint representation of U(N)... that doesn't mean that the a,b indices in the pdf run from 1 to N^2  1 (number of generators)?
what am I misunderstanding here?
thanks!
in the first page of the attached pdf, after the title " 't hooft double line notation", he says that we have to consider the gluon as NxN traceless hermitian matrices to convince ourselves about the double line notation.
there is my question: if you want the indices a,b to run from 1 to N, you need the T^A generators to be NxN matrices, and that means that you are in the fundamental representation, right?
but when you look for a demonstration of the 't hooft's planar limit, it seems that you need the gauge bosons to be in the adjoint representation of U(N)... that doesn't mean that the a,b indices in the pdf run from 1 to N^2  1 (number of generators)?
what am I misunderstanding here?
thanks!
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