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Large-N expansion, conformal field theory and renormalization-group flows in three dimensions

D. Anselmi
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Abstract

I study a class of interacting conformal field theories and conformal windows in three dimensions, formulated using the Parisi large-N approach and a modified dimensional-regularization technique. Bosons are associated with composite operators and their propagators are dynamically generated by fermion bubbles. Renormalization-group flows between pairs of interacting fixed points satisfy a set of non-perturbative g <-> 1/g dualities. There is an exact relation between the beta function and the anomalous dimension of the composite boson. Non-Abelian gauge fields have a non-renormalized and quantized gauge coupling, although no Chern-Simons term is present. A problem of the naive dimensional-regularization technique for these theories is uncovered and removed with a non-local, evanescent, non-renormalized kinetic term. The models are expected to be a fruitful arena for the study of odd-dimensional conformal field theory.

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D. Anselmi. 2000-05-31. Large-N expansion, conformal field theory and renormalization-group flows in three dimensions. https://doi.org/10.1088/1126-6708%2F2000%2F06%2F042

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