On first order formulations of supergravities

TL;DR

This paper introduces a general method to derive pure first-order formulations of supergravity theories from the traditional 1.5 order approach, simplifying symmetry analysis and dimensional reduction studies.

Contribution

It provides a systematic scheme to obtain first-order supergravity formulations from 1.5 order ones, including new results for N_4=2 and N_11=1 supergravities.

Findings

Derived N_4=1 supergravity in first-order form

Presented new results for N_4=2 and N_11=1 supergravities

Highlighted limitations of auxiliary fields in higher dimensions

Abstract

Supergravities are usually presented in a so-called 1.5 order formulation. Here we present a general scheme to derive pure 1^{st} order formulations of supergravities from the 1.5 order ones. The example of N_4=1 supergravity will be rederived and new results for N_4=2 and N_11=1 will be presented. It seems that beyond four dimensions the auxiliary fields introduced to obtain first order formulations of SUGRA theories do not admit supergeometrical transformation laws at least before a full superfield treatment. On the other hand first order formalisms simplify eventually symmetry analysis and the study of dimensional reductions.