An introduction to supersymmetric field theories in curved space

TL;DR

This paper provides a comprehensive pedagogical overview of constructing and analyzing supersymmetric field theories on curved spacetime using off-shell supergravity backgrounds, applicable across various dimensions and supersymmetry levels.

Contribution

It introduces a systematic framework for supersymmetric theories in curved space, emphasizing off-shell supergravity backgrounds and covering multiple dimensions and supersymmetry types.

Findings

Framework applicable to diverse dimensions and supersymmetry levels

Detailed methods for N=1 theories in four dimensions

Extensions to three-dimensional N=2 supersymmetric theories

Abstract

In this review, we give a pedagogical introduction to a systematic framework for constructing and analyzing supersymmetric field theories on curved spacetime manifolds. The framework is based on the use of off-shell supergravity background fields. We present the general principles, which broadly apply to theories with different amounts of supersymmetry in diverse dimensions, as well as specific applications to N=1 theories in four dimensions and their three-dimensional cousins with N=2 supersymmetry.