Supersymmetric Duality Rotations

Sergei M. Kuzenko; Stefan Theisen (University of Munich)

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Supersymmetric Duality Rotations

Sergei M. Kuzenko, Stefan Theisen (University of Munich)

High Energy Physics - Theory · Submitted 11 Jan 2000

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

The authors' main claim We derive N = 1, 2 superfield equations as the conditions for a (nonlinear) theory of one abelian N = 1 or N = 2 vector multiplet to be duality invariant.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We derive N = 1, 2 superfield equations as the conditions for a (nonlinear) theory of one abelian N = 1 or N = 2 vector multiplet to be duality invariant. The N = 1 super Born-Infeld action is a particular solution of the corresponding equation. A family of duality invariant nonlinear N = 1 supersymmetric theories is described. We present the solution of the N = 2 duality equation which reduces to the N = 1 Born-Infeld action when the (0,1/2) part of N = 2 vector multiplet is switched off. We also propose a constructive perturbative scheme to compute duality invariant N = 2 superconformal actions.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We derive N = 1, 2 superfield equations as the conditions for a (nonlinear) theory of one abelian N = 1 or N = 2 vector multiplet to be duality invariant.	contribution 0.85	0.96	0.61	asserted 1.00
s1	The N = 1 super Born-Infeld action is a particular solution of the corresponding equation.	result 0.95	0.70	0.15	asserted 1.00
s2	A family of duality invariant nonlinear N = 1 supersymmetric theories is described.	contribution 0.56	0.91	0.28	asserted 1.00
s3	We present the solution of the N = 2 duality equation which reduces to the N = 1 Born-Infeld action when the (0,1/2) part of N = 2 vector multiplet is switched off.	result 0.87	0.93	0.20	asserted 1.00
s4	We also propose a constructive perturbative scheme to compute duality invariant N = 2 superconformal actions.	contribution 0.49	0.89	0.13	asserted 0.51

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The paper

Original abstract

We derive N = 1, 2 superfield equations as the conditions for a (nonlinear) theory of one abelian N = 1 or N = 2 vector multiplet to be duality invariant. The N = 1 super Born-Infeld action is a particular solution of the corresponding equation. A family of duality invariant nonlinear N = 1 supersymmetric theories is described. We present the solution of the N = 2 duality equation which reduces to the N = 1 Born-Infeld action when the (0,1/2) part of N = 2 vector multiplet is switched off. We also propose a constructive perturbative scheme to compute duality invariant N = 2 superconformal actions.

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References

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Cited by 10 Pith papers

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

Exact Stress Tensor Flows in Causal Electrodynamics: Courant-Hilbert Approach
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Compensator-free $\mathcal N=2$ extension of ModMax and scalar propagation
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A compensator-free N=2 superconformal and duality-invariant extension of ModMax electrodynamics is constructed as a formal series, with causal scalar propagation on constant electromagnetic backgrounds.
Integrable auxiliary field sigma model and the metric approach to $T\bar{T}$-like deformations
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The paper unifies the auxiliary-field and metric descriptions of T̅T-like deformations of integrable sigma models and proves that only T̅T, among Lorentz-invariant deformations, is a field-dependent coordinate change.
Heat kernel approach to the one-loop effective action for nonlinear electrodynamics
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On Covariant Actions for Chiral $p-$Forms
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A polynomial, Lorentz-covariant action for free chiral p-forms is presented, equivalent to PST and featuring an auxiliary p-form.

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ModMax meets Susy
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A single superspace integral supersymmetrizes any convex nonlinear electrodynamics theory, yielding a superModMax theory that preserves electromagnetic duality and superconformal invariance.
On p-form gauge theories and their conformal limits
hep-th 2020-12 accept novelty 6.0 of 10

A new family of six-dimensional chiral two-form gauge theories is constructed whose weak- and strong-field limits are the only conformal possibilities, and its dimensional reduction produces new duality-invariant theo...
On the Goldstino actions and their symmetries
hep-th 2011-02 accept novelty 6.0 of 10

All known Goldstino actions are shown to be one theory written in different field coordinates, connected by an explicit 32-parameter family of field redefinitions modulo a 12-parameter group of trivial symmetries.
On Current-Squared Flows and ModMax Theories
hep-th 2022-03 accept novelty 5.0 of 10

The Born-Infeld-ModMax Lagrangian satisfies a stress-tensor-squared flow equation for any value of the ModMax parameter, and its N=1 supersymmetric version satisfies a supercurrent-squared flow.
Manifestly duality-invariant interactions in diverse dimensions
hep-th 2019-08 conditional novelty 5.0 of 10

For a gauge (2p-1)-form in d=4p dimensions, a U(1) duality-invariant theory is reformulated so that the self-interactions of an auxiliary tensor are manifestly U(1) invariant.

How the literature uses it

44 arXiv papers cite this in 148 sentences

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Papers citing it · 104 sentences without a confident label

Builds on it 7 papers

Finally, we give a new realization for the duality-invariant $=2$ supersymmetric theories presented in [ref] .

Duality rotations in supersymmetric nonlinear electrodynamics revisited · Duality rotations in $=2$ supersymmetric nonlinear electrodynamics · 0.93
Here we consider a generalization of the $N=0$ and $N=1$ actions assuming—as in [ref] —dependence on the $=2$ superfields $^2$ and $^2$.

N=2 Supersymmetry and U(1)-Duality · $N=2$ SUSY, $U(1)$ duality, and derivative requirements · 0.93
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

Uses its method or tool 2 papers

To study duality symmetries one has to use the Noether-Gaillard-Zumino type construction [ref] , which provides the conserved current for such symmetries and guaranties that the equations of motion are duality invariant.[The bona fide Noether current of the Lorentz non-covariant version of the theory developed in [ref] and the Hamiltonian approach in [ref] may be used for an alternative analysis of the UV properties of $N=8$ supergravity. ] In application to $N=8$ supergravity, the current of the classical theory was constructed explicitly in [ref] by embedding $E_7(7)$ into $Sp(2n,ℝ)$.

E{7(7)} Symmetry and Finiteness of N=8 Supergravity · Introduction · 0.93
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

Compares with it 6 papers

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
This agrees with the perturbative solution derived in [ref] .

Superconformal duality-invariant models and $\mathcal{N} = 4$ SYM effective action · Superconformal duality-invariant models in flat space · 0.97
This equation is formally identical to the condition on the bosonic Lagrangian density required for duality invariance of its EL equations [ref] .

ModMax meets Susy · Duality invariance · 0.90

Cites it as background 18 papers

Last but not least, an approach was developed in [ref] .

On the road to N=2 supersymmetric Born-Infeld action · Introduction · 0.95
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
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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