Physical auxiliary field in supersymmetric QCD with explicit supersymmetry breaking

TL;DR

This paper demonstrates that in supersymmetric QCD with explicit supersymmetry breaking, the auxiliary field can be interpreted as a physical degree of freedom, with its vacuum expectation value linked to quark bilinear operators.

Contribution

It reveals that the auxiliary field becomes a physical degree of freedom under explicit supersymmetry breaking and connects its vacuum expectation value to non-perturbative quark bilinear operators.

Findings

Auxiliary field can be a physical degree of freedom in broken SUSY.

Vacuum expectation value remains finite as squark mass becomes infinite.

Large N_c limit is necessary for effective Kaehler potential approximation.

Abstract

It is shown that the auxiliary field in the low-energy effective theory of the supersymmetric QCD (SU(N_c) gauge symmetry with flavors N_f < N_c) can be understood as a physical degree of freedom, once the supersymmetry is explicitly broken. Although the vacuum expectation value of the auxiliary field is just a measure of the supersymmetry breaking in the perturbative treatment of the supersymmetry breaking, it can be the vacuum expectation value of the quark bilinear operator in the non-perturbative treatment of the supersymmetry breaking. We show that the vacuum expectation value remains finite in the limit of the infinite supersymmetry-breaking mass of the squark. We have to take the large N_c limit simultaneously to keep the low-energy effective Kaehler potential being in good approximation.