Four loop wave function renormalization in the non-abelian Thirring model Original Research Article

We compute the anomalous dimension of the fermion field with Nf flavours in the fundamental representation of a general Lie colour group in the non-abelian Thirring model at four loops. The implications on the renormalization of the two point Greenʹs function through the loss of multiplicative renormalizability of the model in dimensional regularization due to the appearance of evanescent four fermi operators are considered at length. We observe the appearance of one new colour group Casimir, dFabcddFabcd, in the final four loop result and discuss its consequences for the relation of the Knizhnik–Zamolodchikov critical exponents in the Wess–Zumino–Witten–Novikov model to the non-abelian Thirring model. Renormalization scheme changes are also considered to ensure that the underlying Fierz symmetry broken by dimensional regularization is restored.