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On Fermion Masses, Gradient Flows and Potential in Supersymmetric Theories
High Energy Physics - Theory · Submitted 19 Mar 2001
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In any low energy effective supergravity theory general formulae exist which allow one to discuss fermion masses, the scalar potential and breaking of symmetries in a model independent set up.
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In any low energy effective supergravity theory general formulae exist which allow one to discuss fermion masses, the scalar potential and breaking of symmetries in a model independent set up. A particular role in this discussion is played by Killing vectors and Killing prepotentials. We outline these relations in general and specify then in the context of N=1 and N=2 supergravities in four dimensions. Useful relations of gauged quaternionic geometry underlying hypermultiplets dynamics are discussed.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In any low energy effective supergravity theory general formulae exist which allow one to discuss fermion masses, the scalar potential and breaking of symmetries in a model independent set up. | background 0.99 | 0.08 | 0.18 | asserted 1.00 |
| s1 | A particular role in this discussion is played by Killing vectors and Killing prepotentials. | background 0.95 | 0.08 | 0.06 | asserted 1.00 |
| s2 | We outline these relations in general and specify then in the context of N=1 and N=2 supergravities in four dimensions. | contribution 0.92 | 0.82 | 0.10 | asserted 0.96 |
| s3 | Useful relations of gauged quaternionic geometry underlying hypermultiplets dynamics are discussed. | contribution 0.93 | 0.58 | 0.07 | asserted 0.96 |
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Original abstract
In any low energy effective supergravity theory general formulae exist which allow one to discuss fermion masses, the scalar potential and breaking of symmetries in a model independent set up. A particular role in this discussion is played by Killing vectors and Killing prepotentials. We outline these relations in general and specify then in the context of N=1 and N=2 supergravities in four dimensions. Useful relations of gauged quaternionic geometry underlying hypermultiplets dynamics are discussed.
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21 arXiv papers cite this in 37 sentences
Papers citing it · 26 sentences without a confident label
Cites it as background 10 papers
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Furthermore, the $Ω^x$ are identified with the field strength of the $SU(2)$ part of the holonomy group and as a consequence they are covariantly constant with respect to the $SU(2)$ connection: $∇_wΩ^x_uv=0$.[Strictly speaking $Ω^x$ only needs to be proportional to the Hyperkähler two-forms but in order to simplify the notation we have chosen the proportionality factor to be equal to $-1$, as is usually done in the literature (corresponding to $λ=-1$ in [ref] and $ν= -2$ in [ref] ).] Here and in the following, $∇_u$ denotes a covariant derivative involving also the $SU(2)$ connection.
No metastable de Sitter vacua in N=2 supergravity with only hypermultiplets · Preliminaries · 0.81
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Here we give properties of the quaternionic Kahler manifold $M _QK$ useful in the study of the $𝒩=2$ gauged supergravity [ref] ; this is a real $4n_H$- dimensional Riemanian variety having an $SU(2)_R×G^'$ holonomy group with $G^'$ contained in a symplectic group as follows [equation] Notice that the combination of the $SU(2)_R$ symmetry of $M _QK$ with the $U(1)_R$ Kahler group of $M_SK$ define the usual $U(2)_R=U(1)_R×SU(2)_R$ R-symmetry of the $𝒩=2$ supersymmetric algebra [equation]
Partial Breaking in Rigid Limit of $\mathcal{N}=2$ Gauged Supergravity · Quaternionic Kahler Manifolds · 0.98
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For the derivation of what follows we refer the reader to the original works we used [ref] and to the very nice review [ref] .
The unbearable lightness of charged gravitini · Basic Ingredients of 4D N=2 gauged supergravity · 0.94
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