Harmonic forms on asymptotically ADS metrics

Guido Franchetti; Raúl Sánchez Galán

doi:10.1088/1751-8121/ac8a29

Harmonic forms on asymptotically ADS metrics

Guido Franchetti
, Raúl Sánchez Galán

Department of Mathematical Sciences

Nanjing University of Science and Technology

Research output: Contribution to journal › Article › peer-review

1 Citation (SciVal)

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
Article number	385205
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	55
Issue number	38
Early online date	31 Aug 2022
DOIs	https://doi.org/10.1088/1751-8121/ac8a29
Publication status	Published - 23 Sept 2022

Bibliographical note

Funding Information:
GF thanks the Simons Foundation for its support under the Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics (Grant 488631).

Funding

GF thanks the Simons Foundation for its support under the Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics (Grant 488631).

Keywords

harmonic cohomology
Killing spinors
supergravity

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Modelling and Simulation
Mathematical Physics
General Physics and Astronomy

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10.1088/1751-8121/ac8a29Licence: CC BY

Cite this

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title = "Harmonic forms on asymptotically ADS metrics",

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.",

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author = "Guido Franchetti and \{S{\'a}nchez Gal{\'a}n\}, Ra{\'u}l",

note = "Funding Information: GF thanks the Simons Foundation for its support under the Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics (Grant 488631). ",

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AU - Franchetti, Guido

AU - Sánchez Galán, Raúl

N1 - Funding Information: GF thanks the Simons Foundation for its support under the Simons Collaboration on Special Holonomy in Geometry, Analysis and Physics (Grant 488631).

PY - 2022/9/23

Y1 - 2022/9/23

N2 - 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.

AB - 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.

KW - harmonic cohomology

KW - Killing spinors

KW - supergravity

UR - https://www.scopus.com/pages/publications/85137647111

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DO - 10.1088/1751-8121/ac8a29

M3 - Article

AN - SCOPUS:85137647111

SN - 1751-8113

VL - 55

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 38

M1 - 385205

ER -

Harmonic forms on asymptotically ADS metrics

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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