Three-loop singularity structure of a principal chiral field model

The talk is devoted to the three-loop renormalization of the effective action for a two-dimensional principal chiral field model using the background field method and a cut-off regularization in the coordinate representation. The coefficients of the renormalization constant and the necessary auxiliary vertices are found. Asymptotic expansions for all three-loop diagrams and their dependence on the type of regularization function are also studied.