The finite two-loop effective action in the N = 1 supersymmetric sigma-model

Abstract

The finite two-loop effective action of the N = 1 supersymmetric non-linear σ-model is investigated. Two distict regulating schemes, operator regularization and dimensional regularization, are employed to compute this quantity. The superfield formalism is used in our analysis in conjunction with an infrared (IR) regulating mass; we point out that operator regularization manifestly preserves all manipulations involving the D-algebra. The β-function is derived from the application of the renormalization group equation to the finite effective action. We find that the β-function is both method-dependent and sensitive to the IR mass-limit and that the renormalization group equation is not consistent. It is possible to perform a finite renormalization on the one-loop Green's functions to make the effective action method-independent at the price of introducing a one-parameter scheme dependence. Neither the inconsistency of the renormalization group equation nor the IR mass-limit problem are affected by this operation. By introducing a generalized mass-potential with off-diagonal terms, the latter problem may be treated: we show that the vanishing of the β-function to two-loop order then becomes insensitive to the IR mass-limit and agrees with previous results in each method.