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I have been reading the paper "Quantum Gravity with a Positive Cosmological Constant" by Lee Smolin (http://arxiv.org/abs/hep-th/0209079), and am having some trouble making the constants in Part I, Sections 2, 3, and 4 match with what I would calculate them to be when I try to go through the derivations for myself. I wondered if anyone else has gone through these derivations and knows if there are typos or maybe a different normalization convention for Levi-Civita symbol than what I am used to (+-1), or if I am making some mistake? Please help! I have gone through the calculations several times and am not sure what is going wrong.

Thank you!!