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On the Bogomol'nyi bound in Einstein-Maxwell-dilaton gravity
High Energy Physics - Theory · Submitted 1 Nov 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This implies that the theory with $\alpha \ne 0, \sqrt 3$ cannot be embedded into supergravity except for the static truncation.
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The abstract, sentence by sentence
It has been shown that the 4-dimensional Einstein-Maxwell-dilaton theory allows a Bogomol'nyi-type inequality for an arbitrary dilaton coupling constant $\alpha $, and that the bound is saturated if and only if the (asymptotically flat) spacetime admits a nontrivial spinor satisfying the gravitino and the dilatino Killing spinor equations. The present paper revisits this issue and argues that the dilatino equation fails to ensure the dilaton field equation unless the solution is purely electric/magnetic, or the dilaton coupling constant is given by $\alpha=0, \sqrt 3$, corresponding to the Brans-Dicke-Maxwell theory and the Kaluza-Klein reduction of 5-dimensional vacuum gravity, respectively. A systematic classification of the supersymmetric solutions reveals that the solution can be rotating if and only if the solution is dyonic or the coupling constant is given by $\alpha=0, \sqrt 3$. This implies that the theory with $\alpha \ne 0, \sqrt 3$ cannot be embedded into supergravity except for the static truncation. Physical properties of supersymmetric solutions are explored from various points of view.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | It has been shown that the 4-dimensional Einstein-Maxwell-dilaton theory allows a Bogomol'nyi-type inequality for an arbitrary dilaton coupling constant $\alpha $, and that the bound is saturated if and only if the (asymptotically flat) spacetime admits a nontrivial spinor satisfying the gravitino and the dilatino Killing spinor equations. | background 1.00 | 0.06 | 0.07 | asserted 1.00 |
| s1 | The present paper revisits this issue and argues that the dilatino equation fails to ensure the dilaton field equation unless the solution is purely electric/magnetic, or the dilaton coupling constant is given by $\alpha=0, \sqrt 3$, corresponding to the Brans-Dicke-Maxwell theory and the Kaluza-Klein reduction of 5-dimensional vacuum gravity, respectively. | result 0.83 | 0.77 | 0.58 | asserted 0.81 |
| s2 | A systematic classification of the supersymmetric solutions reveals that the solution can be rotating if and only if the solution is dyonic or the coupling constant is given by $\alpha=0, \sqrt 3$. | result 0.99 | 0.87 | 0.21 | asserted 1.00 |
| s3 | This implies that the theory with $\alpha \ne 0, \sqrt 3$ cannot be embedded into supergravity except for the static truncation. | interpretation 0.96 | 0.75 | 0.51 | asserted 0.97 |
| s4 | Physical properties of supersymmetric solutions are explored from various points of view. | contribution 0.99 | 0.76 | 0.03 | asserted 0.53 |
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The paper
Original abstract
It has been shown that the 4-dimensional Einstein-Maxwell-dilaton theory allows a Bogomol'nyi-type inequality for an arbitrary dilaton coupling constant $\alpha $, and that the bound is saturated if and only if the (asymptotically flat) spacetime admits a nontrivial spinor satisfying the gravitino and the dilatino Killing spinor equations. The present paper revisits this issue and argues that the dilatino equation fails to ensure the dilaton field equation unless the solution is purely electric/magnetic, or the dilaton coupling constant is given by $\alpha=0, \sqrt 3$, corresponding to the Brans-Dicke-Maxwell theory and the Kaluza-Klein reduction of 5-dimensional vacuum gravity, respectively. A systematic classification of the supersymmetric solutions reveals that the solution can be rotating if and only if the solution is dyonic or the coupling constant is given by $\alpha=0, \sqrt 3$. This implies that the theory with $\alpha \ne 0, \sqrt 3$ cannot be embedded into supergravity except for the static truncation. Physical properties of supersymmetric solutions are explored from various points of view.
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How the literature uses it
10 arXiv papers cite this in 15 sentences
Papers citing it · 13 sentences without a confident label
Cites it as background 2 papers
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Generalizing earlier work by Tod [ref] , the seminal paper by Gauntlett et. al [ref] has triggered many new developments in this field, cf. [ref] for an (incomplete) list of references.
Geometry of Killing spinors in neutral signature · Introduction · 0.88
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While holography of such black holes have already been studied, (see. e.g. [ref] ), complication may arise since dyonic dilaton black hole solutions cannot be embedded into supergravity theory except for $α=0,√(3)$ [ref] .
Stringy Stability of Charged Dilaton Black Holes with Flat Event Horizon · Discussion · 0.90
What it cites · 38 sentences without a confident label
Uses the method or tool of 3 papers
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Reference [ref] also introduced the “variation of dilatino” by[ Note that the conventions of the present paper differs from [ref] , where the gamma matrix and the Dirac conjugate are defined by ${γ_μ,γ_ν}=-2g_μν$ and $ψ̅=ψ^†γ^0$.
Supersymmetric Self-Gravitating Solitons · BPS inequality · 0.87
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Given a commuting spinor $ϵ$, we can define the following bilinear bosonic differential forms [ref]
All Supersymmetric Solutions of N=2, D=4 Gauged Supergravity · Differential forms constructed from a Killing spinor · 0.93
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In the classification procedure we adopt a prescription of [ref] , which is adequate also in the proof for the variant of positive energy theorem described below.
All supersymmetric solutions of minimal supergravity in five dimensions · Introduction · 1.00
Compares with 1 paper
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In reference [ref] , a different expression of the Bogomol'nyi-type bound [equation] is conjectured from the force-balance point of view.
The Rotating Dyonic Black Holes Of Kaluza-Klein Theory · BPS inequality · 0.80
Cites as support 1 paper
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The result [ref] strongly implies that the the theory ([ref]) can be “gauged” to include the exponential Liouville-type potential.
Cosmological rotating black holes in five-dimensional fake supergravity · Concluding remarks · 0.96
Cites as background 7 papers
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Thereafter the classification program has achieved a remarkable development in diverse supergravities in various dimensions [ref] .
The Geometry of D=11 Killing Spinors · Introduction · 0.90
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Thereafter the classification program has achieved a remarkable development in diverse supergravities in various dimensions [ref] .
All supersymmetric solutions of minimal gauged supergravity in five dimensions · Introduction · 0.90
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Thereafter the classification program has achieved a remarkable development in diverse supergravities in various dimensions [ref] .
All supersymmetric solutions of minimal supergravity in six dimensions · Introduction · 0.90
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