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I'm trying to read through a paper which explains the following about Universal Extra Dimensions (UED) vs ADD models:

The new feature of the UED scenario compared to the brane world is that since there is no brane to violate translation invariance along the extra dimensions, momentum is conserved at tree level leading to degenerate KK mode masses at each level and conservation of KK number in the interactions of the four dimensional effective theory. This statement is broken at the loop level, where the fact that the extra dimensions are compact leads to (calculable) violations of the full Lorentz symmetry, and as a result shifts the masses of the KK modes away from their tree level values.

I'm unfamiliar with the concepts of tree-level and loop-level. Could someone perhaps explain this in context? If I would have to guess, I'm thinking that tree-level correspond to the scattering correlation functions of the classical theory and loop-level are a kind of correction?

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"I'm thinking that tree-level correspond to the scattering correlation functions of the classical theory and loop-level are a kind of correction?" Indeed you are right. The terminology comes from quantum field theory and refers to Feynman diagrams. Tree-like Feynman diagrams give the leading order terms in perturbation theory and the loop diagrams come in with a factor of $\hbar$ for each loop. This is developed in any book or decent set of lecture notes on QFT. :) –  Michael Brown Jun 12 '13 at 14:35
    
Thanks, just needed to get a sanity check :) –  adnan Jun 12 '13 at 14:38

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