Vector non-Abelian Chern-Simons duality

Abstract

Abelian Chern-Simons gauge theory is known to possess an $``S\ensuremath{-}\mathrm{s}\mathrm{e}\mathrm{l}\mathrm{f}\ensuremath{-}\mathrm{d}\mathrm{u}\mathrm{a}\mathrm{l}''$ action where its coupling constant k is inverted, i.e., $k\ensuremath{\leftrightarrow}1/k.$ Here a vector non-Abelian duality is found in the pure non-Abelian Chern-Simons action at the classical level. The dimensional reduction of the dual Chern-Simons action to two dimensions constitutes a dual Wess-Zumino-Witten action already given in the literature.