Gauging Isometries on Hyperkahler Cones and Quaternion-Kahler Manifolds

Bernard de Wit; Martin Rocek; Stefan Vandoren

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Gauging Isometries on Hyperkahler Cones and Quaternion-Kahler Manifolds

Bernard de Wit, Martin Rocek, Stefan Vandoren

High Energy Physics - Theory · Submitted 24 Apr 2001

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We extend our previous results on the relation between quaternion-Kahler manifolds and hyperkahler cones and we describe how isometries, moment maps and scalar potentials descend from the cone to the quaternion-Kahler space.

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arXiv IDhep-th/0104215 (version 1)

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CitationBernard de Wit, Martin Rocek, Stefan Vandoren. "Gauging Isometries on Hyperkahler Cones and Quaternion-Kahler Manifolds." arXiv:hep-th/0104215 (2001). https://pith.science/paper/QZDUVAW2

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.48 · mentions code or data availability 0.01.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We extend our previous results on the relation between quaternion-Kahler manifolds and hyperkahler cones and we describe how isometries, moment maps and scalar potentials descend from the cone to the quaternion-Kahler space. As an example of the general construction, we discuss the gauging and the corresponding scalar potential of hypermultiplets with the unitary Wolf spaces as target spaces. This class includes the universal hypermultiplet.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We extend our previous results on the relation between quaternion-Kahler manifolds and hyperkahler cones and we describe how isometries, moment maps and scalar potentials descend from the cone to the quaternion-Kahler space.	contribution 1.00	0.89	0.54	asserted 1.00
s1	As an example of the general construction, we discuss the gauging and the corresponding scalar potential of hypermultiplets with the unitary Wolf spaces as target spaces.	contribution 0.92	0.89	0.13	asserted 0.97
s2	This class includes the universal hypermultiplet.	interpretation 0.41	0.27	0.05	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 0.99.

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The paper

Original abstract

We extend our previous results on the relation between quaternion-Kahler manifolds and hyperkahler cones and we describe how isometries, moment maps and scalar potentials descend from the cone to the quaternion-Kahler space. As an example of the general construction, we discuss the gauging and the corresponding scalar potential of hypermultiplets with the unitary Wolf spaces as target spaces. This class includes the universal hypermultiplet.

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References

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

(1,0) superconformal models in six dimensions
hep-th 2011-08 accept novelty 7.0 of 10

Six-dimensional (1,0) superconformal models with non-abelian charged tensor multiplets exist, built from a p-form tensor hierarchy whose three-form potentials mediate the vector-tensor coupling.
Membrane and fivebrane instantons and quaternonic geometry
hep-th 2006-03 conditional novelty 7.0 of 10

The paper derives fivebrane and membrane instanton corrections to the universal hypermultiplet moduli space metric in type IIA string theory, using instanton calculus and Toda equation solutions.
D-instantons and twistors
hep-th 2008-12 conditional novelty 6.0 of 10

All D-instanton corrections to the hypermultiplet moduli space metric in Type II Calabi-Yau compactifications can be packaged as a sum of dilogarithms controlled by a single holomorphic function, in the leading instan...
Magnetic charges in local field theory
hep-th 2005-07 conditional novelty 6.0 of 10

A single gauge-invariant four-dimensional Lagrangian can contain both electric and magnetic non-abelian vector potentials, provided rank-2 tensor fields with their own gauge symmetry are included to keep the degree-of...
Quaternion-Kahler spaces, hyperkahler cones, and the c-map
math.DG 2006-03 conditional novelty 4.0 of 10

The hyperkähler cone of a c-map quaternion-Kähler space is determined by the special Kähler prepotential through H = F(η^I)/η^0, yielding an explicit hyperkähler potential.

How the literature uses it

21 arXiv papers cite this in 30 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 18 sentences without a confident label

Builds on it 1 paper

These results extend those of [ref] and agree with the findings of [ref] .

Quaternionic Kahler spaces with large toric symmetry · Tri-Hamiltonian actions · 0.88

Uses its method or tool 1 paper

We use the formalism from [ref] with the vector prepotential [equation]

On NS5-brane instantons and volume stabilization · Potentials in $N=2$ · 1.00

Compares with it 1 paper

Substituting the corresponding values of $κ^2$ and $a$, one can check that the scalar potential [ref] agrees with the one given in [ref] , but differs by the factor of $1/4$ from those in [ref] .

Non-perturbative scalar potential inspired by type IIA strings on rigid CY · Quaternionic geometry and scalar potential · 1.00

Cites it as background 8 papers

Rigid superconformal sigma-models in three dimensions have recently been constructed in component formalism [ref] building on earlier works [ref] .

Off-shell superconformal nonlinear sigma-models in three dimensions · Introduction · 0.93
In the general expression for the $𝒩=2$ scalar potential, there is an additional term proportional to the quaternionic moment maps (see e.g. [ref] ) [equation] These moment maps in turn are proportional to a covariant derivative on $k̃^u_Λ$.

New potentials from Scherk-Schwarz reductions · Scalar potential · 0.80
As is well-known, a $4(n+1)$-dimensional hyperkähler cone is in one-to-one correspondence with a $4n$-dimensional quaternion-Kähler manifold [ref] (see also [ref] ).

On conformal supergravity and harmonic superspace · Quaternion-Kähler superspace · 0.85

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