Integration of massive states as contractions of non linear $\sigma$-models

TL;DR

This paper studies how contracting non-linear sigma models can effectively describe integrating out massive modes in supergravity theories, especially after supersymmetry breaking, providing a new mathematical approach to model reduction.

Contribution

It introduces a contraction method for non-linear sigma models that captures the integration of massive modes in supergravity theories with mass deformations.

Findings

Contraction of sigma models corresponds to integrating out massive modes.

The method applies to models with spontaneous supersymmetry breaking.

Provides a mathematical framework for effective supergravity actions.

Abstract

We consider the contraction of some non linear sigma models which appear in effective supergravity theories. In particular we consider the contractions of maximally symmetric spaces corresponding to N=1 and N=2 theories, as they appear in certain low energy effective supergravity actions with mass deformations. The contraction procedure is shown to describe the integrating out of massive modes in the presence of interactions, as it happens in many supergravity models after spontaneous supersymmetry breaking.