Higher Derivative Supergravities in Diverse Dimensions

TL;DR

This paper surveys higher derivative supergravity theories across dimensions 1 to 11, discussing their construction methods, supersymmetric solutions, and the role of duality symmetries, providing a comprehensive overview of the field.

Contribution

It compiles various construction approaches and analyzes supersymmetric solutions and duality roles in higher derivative supergravities across multiple dimensions.

Findings

Summarizes methods like Noether procedure, superspace, superform, and superconformal calculus.

Provides explicit bosonic invariants and supertransformations.

Reviews solutions to Killing spinor equations and duality symmetries in higher derivative invariants.

Abstract

We survey on-shell and off-shell higher derivative supergravities in dimensions $1\le D\le 11$. Various approaches to their construction, including the Noether procedure, (harmonic) superspace, superform method, superconformal tensor calculus, $S$-matrix and dimensional reduction, are summarized. Primarily the bosonic parts of the invariants and the supertransformations of the fermionic fields are provided. The process of going on-shell, solutions to the Killing spinor equations, typical supersymmetric solutions, and the role of duality symmetries in the context of $R^4, D^4 R^4$ and $D^6 R^4$ invariants are reviewed.