The symmetries of five-dimensional minimal supergravity reduced to three dimensions

TL;DR

This paper explicitly constructs the 14 Killing vectors of the target space in five-dimensional minimal supergravity reduced to three dimensions, revealing the underlying $G_2$ symmetry and providing a matrix representative of the coset structure.

Contribution

It explicitly constructs the Killing vectors and the matrix representative of the coset $G_{2(+2)}/(SL(2,R) imes SL(2,R))$ in five-dimensional minimal supergravity reduced to three dimensions.

Findings

Identified the 14 Killing vectors generating the $G_2$ Lie algebra.

Constructed a symmetric $7\times7$ matrix for the coset.

Explicitly expressed these structures in terms of original field variables.

Abstract

The 14 Killing vectors of the target space for five-dimensional minimal supergravity reduced to three dimensions are explicitly constructed in terms of the original field variables. These vectors generate the Lie algebra of $G_2$. We also construct a symmetrical $7\times7$ matrix representative of the coset $G_{2(+2)}/((SL(2,R)\times SL(2,R))$ as a function of the same fields.