## Abstract

In this paper we study the rotationally invariant harmonic cohomology of a two-parameter family of Einstein metrics g which admits a cohomogeneity one action of SU(2) × U(1) and has AdS asymptotics. Depending on the values of the parameters, g is either of NUT type, if the fixed-point locus of the U(1) action is zero-dimensional, or of bolt type, if it is two-dimensional. We find that if g is of NUT type then the space of SU(2)-invariant harmonic two-forms is three-dimensional and consists entirely of self-dual forms; if g is of bolt type it is four-dimensional. In both cases we explicitly determine a basis. The pair (g, F) for F a self-dual harmonic two-form is also a solution of the bosonic sector of 4D supergravity. We determine for which choices it is a supersymmetric solution and the amount of preserved supersymmetry.

Original language | English |
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Article number | 385205 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 55 |

Issue number | 38 |

Early online date | 31 Aug 2022 |

DOIs | |

Publication status | Published - 23 Sept 2022 |

## Keywords

- harmonic cohomology
- Killing spinors
- supergravity

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)