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I've been reading about the duality cascade in Strassler's TASI '03 lectures (hep-th/0505153). He reminds us of the non-renormalization theorem theorem for the superpotential so that the beta functions for superpotential couplings go like their classical scaling dimension plus anomalous dimension terms from wavefunction renormalization. This allows us to make statements about the behavior of these terms even when a theory become strongly coupled, e.g. when the anomalous dimension becomes large. For example, we can say if an operator becomes 'dangerous irrelevant': it is irrelevant classically, but becomes relevant in the deep IR.

In light of the existence of such behavior at strong coupling, I am confused why we can disregard higher order terms that may be generated in the Kahler potential. The Kahler potential has no protection against renormalization, so I would expect higher order classically irrelevant terms to be generated---how do I know that these do not become 'dangerous irrelevant' in the strongly coupled deep IR regime?

More importantly, how do I know that these higher order Kahler potential terms (if they exist) do not destabilize the fixed points of the superpotential couplings that were important for analyzing the duality cascade?


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