Clockwork SUSY: Supersymmetric Ward and Slavnov-Taylor Identities At Work in Green's Functions and Scattering Amplitudes

TL;DR

This paper investigates how supersymmetric Ward and Slavnov-Taylor identities ensure consistency in quantum field theory calculations, highlighting the persistent role of ghosts and providing tools for verifying supersymmetry in computations.

Contribution

It demonstrates that Faddeev-Popov ghosts do not decouple in supersymmetric theories and shows how Slavnov-Taylor identities can serve as practical checks for supersymmetry in calculations.

Findings

Ghosts do not decouple in supersymmetric theories.

Slavnov-Taylor identities can verify supersymmetry of Feynman rules.

These identities help ensure numerical stability in predictions.

Abstract

We study the cancellations among Feynman diagrams that implement the Ward and Slavnov-Taylor identities corresponding to the conserved supersymmetry current in supersymmetric quantum field theories. In particular, we show that the Faddeev-Popov ghosts of gauge- and supersymmetries never decouple from the physical fields, even for abelian gauge groups. The supersymmetric Slavnov-Taylor identities provide efficient consistency checks for automatized calculations and can verify the supersymmetry of Feynman rules and the numerical stability of phenomenological predictions simultaneously.