Superspace approach to the renormalization of the O'Raifeartaigh model up to the second order in the LDE parameter

TL;DR

This paper uses a superspace formalism and linear delta expansion to analyze divergences in the O'Raifeartaigh model, confirming that only the Kähler potential is renormalized up to second order.

Contribution

It introduces the LDE method into superspace supergraph calculations for the O'Raifeartaigh model and verifies renormalization properties up to second order.

Findings

Only the Kähler potential is renormalized.

Supergraph calculations confirm nonrenormalization of the matter potential.

Renormalization is consistent with supersymmetry theorems.

Abstract

We adopt a superspace/supergraph formalism to pursue the investigation of the structure of one- and two-loop divergences in the frame of the minimal O'Raifeartaigh model that realizes the F-term spontaneous supersymmetry breaking. The linear delta expansion(LDE) procedure is introduced and renormalization is carried out up to the second order in the LDE expansion parameter. In agreement with the nonrenormalization theorem for the (chiral/antichiral) matter potential of ${\mathcal N}=1, \ D=4$ supersymmetry, our explicit supergraph calculations confirm that only the K\"{a}hler potential is actually renomalized.