From Linear SUSY to Constrained Superfields

TL;DR

This paper introduces a formalism using constrained superfields in superspace to derive low-energy effective Lagrangians for Goldstinos and related fields, simplifying calculations and providing new insights into SUSY breaking.

Contribution

It develops a novel approach with constrained superfields to systematically derive effective Lagrangians in supersymmetric theories, including strongly coupled cases.

Findings

Exact IR correlation functions in strongly coupled SUSY breaking theories.

Unified description of Goldstino and matter fields via constrained superfields.

Simplified derivation of known and new results in SUSY effective theories.

Abstract

We present a new formalism for finding the low-energy effective Lagrangian of Goldstinos and other fields. This Lagrangian is written using standard superspace and the superfields are constrained to include only the light degrees of freedom. The Goldstino resides in a (constrained) chiral superfield X which is naturally identified at short distances. This allows us to exactly compute the IR behavior of some correlation functions even in strongly coupled theories with SUSY breaking. The Goldstino couplings above the scale of the matter superpartners are determined by identifying X with the standard spurion. At energies below the superpartners' scale, fermions, scalars (including Goldstone bosons) and gauge fields are also described by constrained superfields. Our framework makes it easy to find the leading order terms in the Lagrangian and to control their corrections. It simplifies the derivation of many known results and leads to new ones.