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Nonlinear Self-Duality and Supersymmetry
High Energy Physics - Theory · Submitted 28 Jul 2000
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We explain why the N = 2 supersymmetric actions proposed so far are not the correct world-volume actions for D3 branes in d = 6.
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The abstract, sentence by sentence
We review self-duality of nonlinear electrodynamics and its extension to several Abelian gauge fields coupled to scalars. We then describe self-duality in supersymmetric models, both N = 1 and N = 2. The self-duality equations, which have to be satisfied by the action of any self-dual system, are found and solutions are discussed. One important example is the Born-Infeld action. We explain why the N = 2 supersymmetric actions proposed so far are not the correct world-volume actions for D3 branes in d = 6.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We review self-duality of nonlinear electrodynamics and its extension to several Abelian gauge fields coupled to scalars. | background 0.53 | 0.33 | 0.06 | asserted 0.78 |
| s1 | We then describe self-duality in supersymmetric models, both N = 1 and N = 2. | contribution 0.92 | 0.68 | 0.05 | asserted 0.92 |
| s2 | The self-duality equations, which have to be satisfied by the action of any self-dual system, are found and solutions are discussed. | contribution 0.70 | 0.74 | 0.12 | asserted 1.00 |
| s3 | One important example is the Born-Infeld action. | background 0.75 | 0.11 | 0.04 | asserted 1.00 |
| s4 | We explain why the N = 2 supersymmetric actions proposed so far are not the correct world-volume actions for D3 branes in d = 6. | result 0.63 | 0.58 | 0.34 | asserted 1.00 |
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The paper
Original abstract
We review self-duality of nonlinear electrodynamics and its extension to several Abelian gauge fields coupled to scalars. We then describe self-duality in supersymmetric models, both N = 1 and N = 2. The self-duality equations, which have to be satisfied by the action of any self-dual system, are found and solutions are discussed. One important example is the Born-Infeld action. We explain why the N = 2 supersymmetric actions proposed so far are not the correct world-volume actions for D3 branes in d = 6.
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References
How the literature uses it
53 arXiv papers cite this in 222 sentences
Papers citing it · 158 sentences without a confident label
Contests it 1 paper
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The computation of the action of the $N=(2,0)$, $d=6$ theory [ref] also faced difficulties: it was argued [ref] that the proposed action is not even $N=(1,0)$ supersymmetric and that it is not possible to write down the six dimensional action as an integral over the $N=(1,0)$, $d=6$ superspace or its supersymmetric subspaces.
Component $d=6$ Born-Infeld theory with $N=(2,0)\rightarrow N=(1,0)$ supersymmetry breaking · Introduction · contest 0.82
Builds on it 6 papers
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These $(1)$ duality invariant theories are curved-superspace extensions of the globally supersymmetric systems introduced in [ref] .
Superconformal vector multiplet self-couplings and generalised Fayet-Iliopoulos terms · Introduction · 0.98
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The results of [ref] were generalised to supergravity in [ref] .] The duality group acts on $$ by fractional linear transformations [ref].
Non-compact duality, super-Weyl invariance and effective actions · Quantisation · 0.86
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The formalism of [ref] was extended to duality-invariant theories with higher derivatives[Further aspects of duality-invariant theories with higher derivatives were studied, e.g., in [ref] .] [ref] , as well as to the case of general $U(1)$ duality-invariant $=1$ and $=2$ supersymmetric theories [ref] .
Duality-Invariant Non-linear Electrodynamics and Stress Tensor Flows · Introduction · 0.88
Uses its method or tool 3 papers
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[ref] , with a general action S = 1/4∫d^6z W^2 + 1/4∫d^6z̅ W̅^2 + 1/4 ∫d^8z W^2 W^2 Ł( 1/8 D^2 W^2 , 1/8 D̅^2 W^2 )
Covariant procedures for perturbative non-linear deformation of duality-invariant theories · $N=1$ supersymmetric nonlinear electrodynamics · 0.87
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To verify duality invariance of the BI-like generalization of ModMax, it is convenient to use, following [ref] , the flat superspace counterparts of the variables [ref]: u:= 𝒟^2 W^2=-8(𝕊-ℙ) , u̅ := 𝒟̅^2 W̅^2=-8(𝕊+ℙ) .
ModMax meets Susy · Duality invariance · 0.99
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The implications of this condition are derived in the Appendix, mimicking standard constructions in nonlinear electrodynamics (see, for example, the Appendix in [ref] ).
Self-dual supersymmetric nonlinear sigma models · Duality invariant sigma models · 0.92
Compares with it 4 papers
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In [ref] , terms up to $W^8$ were obtained and they coincided with the terms obtained in [ref] from the condition of the invariance of the action with respect to the spontaneously broken supersymmetry.
Component $d=6$ Born-Infeld theory with $N=(2,0)\rightarrow N=(1,0)$ supersymmetry breaking · Reduction to four dimensional theory · 0.91
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In spite of this, the functional form of their self-duality equations, see [ref] for the vector multiplet and [ref] for the gravitino multiplet, agrees with that of [ref].[There have been a number of publications devoted to solutions of the self-duality equation for the $=2$ vector multiplet [ref] .] This leads us to believe that the latter is somewhat universal.
Self-duality for $\cal N$-extended superconformal gauge multiplets · Concluding comments · 0.82
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To compare our new complete models with the ones in $d=4$, [ref] , will require a separate investigation.
Dirac-Born-Infeld-Volkov-Akulov and Deformation of Supersymmetry · Introduction · 0.90
Cites it as support 2 papers
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This result is not completely surprising; it was shown in [ref] that all solutions of the bosonic NGZ equation have an $N=1$ supersymmetric completion.
Covariant procedures for perturbative non-linear deformation of duality-invariant theories · $N=1$ supersymmetric nonlinear electrodynamics · 1.00
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It follows from [ref] that every self-dual nonlinear electrodynamics is parity invariant [ref] .
Nonlinear self-duality for arbitrary spin, superspin, and supersymmetry type · Self-duality equation in spinor notation · 0.99
Cites it as background 24 papers
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In this discussion of supersymmetry and self-duality we follow mostly the work by Kuzenko and Theisen [ref] and Ketov [ref] .
Covariant procedures for perturbative non-linear deformation of duality-invariant theories · Nonlinear $U(1)$ duality and supersymmetry · 0.84
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Within the GZGR approach or its supersymmetric extensions, a consistent nonlinear deformation of a given $(1)$ duality-invariant theory (say, Maxwell's theory) is typically derived in perturbation theory and requires an infinite number of terms for the deformed action to satisfy the self-duality equation [ref] or its supersymmetric extensions [ref] .
Higher-derivative deformations of the ModMax theory · Introduction · 0.89
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General duality-invariant supersymmetric theories with at most two derivatives at the component level were constructed in [ref] .
Superconformal duality-invariant models and $\mathcal{N} = 4$ SYM effective action · Formulation without auxiliary chiral variables · 0.89
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