Selfdual backgrounds in N=2 five-dimensional Chern-Simons Supergravity

TL;DR

This paper demonstrates that in five-dimensional N=2 Chern-Simons supergravity, selfdual curvatures on four-dimensional manifolds serve as exact solutions when the cosmological constant is tuned to zero through a specific Kaluza-Klein reduction.

Contribution

It introduces a novel solution class in five-dimensional supergravity where selfdual curvatures solve the equations of motion under specific conditions.

Findings

Selfdual curvatures are exact solutions in N=2 supergravity.

Fine-tuning the Kaluza-Klein reduction yields zero cosmological constant.

The solutions are valid on manifolds with selfdual curvature properties.

Abstract

We consider five-dimensional S(2,2|N) Chern-Simons supergravity on M_4 * R . By fine-tuning the Kaluza-Klein reduction to make the 4d cosmological constant equal zero, it is shown that selfdual curvatures on M_4 provide exact solutions to the equations of motion if N=2.