Supertrace formulae for nonlinearly realized supersymmetry

TL;DR

This paper derives a comprehensive supertrace formula for systems with multiple chiral superfields including a nilpotent one, revealing differences from linear supersymmetry and conditions for reduction to simpler models.

Contribution

It presents the first general supertrace formula for systems with nilpotent superfields in both global and local supersymmetry, highlighting its distinctions from linear cases.

Findings

Derived the supertrace formula for nilpotent superfields

Showed the formula differs from scalar-decoupling limits in linear supersymmetry

Reduced the formula to known cases with decoupled sGoldstino

Abstract

We derive the general supertrace formula for a system with $N$ chiral superfields and one nilpotent chiral superfield in global and local supersymmetry. The nilpotent multiplet is realized by taking the scalar-decoupling limit of a chiral superfield breaking supersymmetry spontaneously. As we show, however, the modified formula is not simply related to the scalar-decoupling limit of the supertrace in linearly-realized supersymmetry. We also show that the supertrace formula reduces to that of a linearly realized supersymmetric theory with a decoupled sGoldstino if the Goldstino is the fermion in the nilpotent multiplet.