Lectures by Susskind versus Zee on the ${\rm SU}(5)$ grand unified theory notations

Question

I was comparing two lectures about ${\rm SU}(5)$ grand unified theory.

1. a lecture of Susskind He showed how to write $$(5 \times 5)_{asym}=\bar{10}$$ as

1. a lecture of Zee showed how to write $$(\bar 5 \times \bar 5)_{asym}={10}$$ as

Other than the difference between $$(5 \times 5)_{asym}=\bar{10} \text{ versus } (\bar 5 \times \bar 5)_{asym}={10}$$

My question is that there is also an extra minus sign in Zee's notation? See the $$- \bar u$$ in the 1st row and the 3rd column. I suppose Zee is correct and Susskind missed a minus sign or more signs. Am I understanding it correct?

This post imported from StackExchange Physics at 2020-11-28 23:05 (UTC), posted by SE-user annie marie heart

Comments

I should agree with you... Lenny is notoriously sloppy with signs and such... he is quick, and he assumes anyone can catch his trivial errors. In this case, the color subspace has a Levi-Civita $\epsilon_{rgb}$ structure, so, yes, you need - signs like Zee, or Langacker. People choose orderings and signs most convenient to them, but in the 3x3 color block you focus on, Lenny definitely needs some signs flipped.

This post imported from StackExchange Physics at 2020-11-28 23:05 (UTC), posted by SE-user Cosmas Zachos

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thanks so much!!!

This post imported from StackExchange Physics at 2020-11-28 23:05 (UTC), posted by SE-user annie marie heart