## Archive for May 2000

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 $g \leftrightarrow 1/g$ 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.

JHEP 0006 (2000) 042 | DOI: 10.1088/1126-6708/2000/06/042