Quantum Equivalence of Auxiliary Field Methods in Supersymmetric Theories

TL;DR

This paper demonstrates that quantum corrections cancel in supersymmetric theories, allowing for generalized auxiliary field lagrangians and resolving ambiguities in effective nonlinear lagrangians through auxiliary gauge fields.

Contribution

It proves quantum correction cancellations in supersymmetric path integrals and introduces non-quadratic auxiliary field lagrangians, clarifying the role of auxiliary gauge fields.

Findings

Quantum corrections cancel to all orders in supersymmetric theories.

Generalized auxiliary field lagrangians can be non-quadratic.

Ambiguities in effective lagrangians are resolved with auxiliary gauge fields.

Abstract

Quantum corrections to Legendre transformations are shown to cancel to all orders in supersymmetric theories in path integral formalism. Using this result, lagrangians for auxiliary fields are generalized to non-quadratic forms. In supersymmetric effective nonlinear lagrangians, the arbitrariness due to the existence of quasi Nambu-Goldstone bosons is shown to disappear when local auxiliary gauge fields are introduced.