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I keep hearing that in the large N limit (so I am talking in specific AdS/CFT but more general too I guess) U(N) and SU(N) are isomorphic. So if I construct, say, the ## \mathcal{N}=1 ## SYM Lagrangian in the large N limit, I can take as gauge group both of the ones mentioned above.

Why is this true?

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# Group theory question about the N large limit

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