arXiv subjects

Sergei M. Kuzenko

Publications and source records attributed to Sergei M. Kuzenko.

At least 19 recordsLinked to original sources

arXiv2026

Causal self-dual nonlinear electrodynamics from the Born-Infeld theory

Recently we have proposed a new auxiliary-field formulation for self-dual nonlinear electrodynamics (NLED) which makes use of two building blocks: (i) a seed self-dual theory $L(F_{μν};g)$, where $F_{μν}$ is the electromagnetic field strength and $g$ a duality-invariant coupling constant; and (ii) a scalar potential $W(ψ)$. Our formulation is based on the Lagrangian $ \mathfrak{L}(F_{μν};ψ) = L(F_{μν};ψ) + W(ψ)$, where $ψ$ is an auxiliary scalar field. Integrating out $ψ$, using its equation of motion, one obtains a $\mathsf{U}(1)$ duality-invariant NLED. Different self-dual NLEDs are derived by choosing different potentials $W(ψ)$. In the case that the seed Lagrangian defines the Born-Infeld theory, in this paper we demonstrate that the resulting models for self-dual NLED are causal and provide a general solution of the self-duality equation. We also elaborate on the procedure to relate our formulation to that developed by Russo and Townsend.

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arXiv2026

On nonlinear self-duality in $4p$ dimensions

Building on the earlier work by Araki and Tanii, Aschieri {\it et al.}, and Buratti {\it et al.}, we demonstrate that every model for self-dual nonlinear electrodynamics in four dimensions has a $\mathsf{U}(1)$ duality-invariant extension to $4p>4$ dimensions and construct new self-dual nonlinear theories for a gauge $(2p-1)$-form. We present a family of models for self-dual nonlinear $(2p-1)$-form electrodynamics in which the trace of the energy-momentum tensor determines the flow with respect to a duality-invariant deformation parameter. Finally, we propose the interesting problem of computing the so-called induced action in the case that self-dual $(2p-1)$-form electrodynamics is coupled to dilaton and axion fields and the compact duality group $\mathsf{U}(1)$ is enhanced to the non-compact group $\mathsf{SL}(2, {\mathbb R})$.

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arXiv2026

Euler-Heisenberg actions in higher dimensions

We extend Schwinger's proper-time formalism to provide a method for computing the one-loop effective action for both spinor and scalar quantum electrodynamics in $d=2n>4$ dimensions. We give the closed form expression for the higher-dimensional Euler-Heisenberg Lagrangian, and extract its weak-field approximation in 6, 8 and 10 dimensions. A subsequent analysis of pair production in $d$ dimensions is also given. In the $d=6$ case, we present a composite conformal primary field of dimension $+6$ which determines the contribution of the electromagnetic field to the Weyl anomaly in curved space.

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arXiv2026

Nonlinear self-duality for arbitrary spin, superspin, and supersymmetry type

We review the general formalism of duality rotations for $\cal N$-extended (super)conformal gauge multiplets of arbitrary (super)spin in four dimensions, with ${\cal N} \geq 0$. Self-dual models for a vector field (${\cal N}=0$) and for ${\cal N}=1$ and ${\cal N}=2$ vector supermultiplets are naturally formulated on general (super)gravity backgrounds. For all other (super)spin values, the corresponding self-dual systems are realised on arbitrary conformally flat backgrounds. Every $\mathsf{U}(1)$ duality-invariant model is demonstrated to be self-dual with respect to a Legendre transformation. Methods are described to generate such self-dual models including superconformal ones. We show that every model for self-dual nonlinear electrodynamics admits a higher-spin extension. Throughout the review, we make use of the formalism of conformal (super)space, that is the geometric setting to describe the gauge theory of the (super)conformal group.

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arXiv2026

Gauge-invariant off-shell formulations for 3D massive higher-spin supermultiplets

Making use of the known off-shell formulations for massless higher-spin ${\cal N}=1$ supermultiplets in four dimensions, gauge-invariant off-shell actions for massive higher-spin ${\cal N}=2$ supermultiplets in three dimensions (3D) are derived by Kaluza-Klein reduction in superspace. To illustrate the formalism, we also construct, for the first time, massive gauge-invariant 3D ${\cal N}=2$ supersymmetric counterparts of the linearised actions for the old and new minimal supergravity theories. Our off-shell ${\cal N}=2$ supermultiplets carry a non-zero central charge, and are formulated in 3D ${\cal N}=2$ central charge superspace. The models can be reduced to 3D ${\cal N}=1$ superspace, by integrating out two Grassmann variables, and then consistent reality conditions on the superfields can be imposed. As a result, only two supercharges remain unbroken.

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arXiv2026

Some remarks on invariants

The demand to know the structure of functionally independent invariants of tensor fields arises in many problems of theoretical and mathematical physics, for instance for the construction of interacting higher-order tensor field actions. In mathematical terms the problem can be formulated as follows. Given a semi-simple finite-dimensional Lie algebra $\mathfrak g$ and a $\mathfrak g$-module $V$, one may ask about the structure of the sub-ring of $\mathfrak g$-invariants inside the ring freely generated by the module. We point out how some information about the ring of invariants may be obtained by studying an extended Lie algebra. Numerous examples are given, with particular focus on the difficult problem of classifying invariants of a self-dual 5-form in 10 dimensions.

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arXiv2026

Generalisations of the Russo-Townsend formulation

As a generalisation of the recent construction by Russo and Townsend, we propose a new approach to generate $\mathsf{U}(1)$ duality-invariant models for nonlinear electrodynamics. It is based on the use of two building blocks: (i) a fixed (but otherwise arbitrary) model for self-dual nonlinear electrodynamics with Lagrangian $L(F_{μν};g)$ depending on a duality-invariant parameter $g$; and (ii) an arbitrary potential $W(ψ)$, with $ψ$ an auxiliary scalar field. It turns out that the model $\mathfrak{L}(F_{μν};ψ) = L(F_{μν};ψ) + W(ψ)$ leads to a self-dual theory for nonlinear electrodynamics upon elimination of $ψ$. As an illustration, we work out two examples in which the seed Lagrangian $L(F_{μν};g)$ corresponds to the Born-Infeld model and two particular potentials $W(ψ)$ are chosen such that integrating out $ψ$ gives: (i) the ModMaxBorn theory; and (ii) the ModMax theory. We also briefly discuss supersymmetric generalisations of the proposed formulation.

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arXiv2026

Duality-invariant (super)conformal higher-spin models

We develop a general formalism of duality rotations for bosonic conformal spin-$s$ gauge fields, with $s\geq 2$, in a conformally flat four-dimensional spacetime. In the $s=1$ case this formalism is equivalent to the theory of $\mathsf{U}(1)$ duality-invariant nonlinear electrodynamics developed by Gaillard and Zumino, Gibbons and Rasheed, and generalised by Ivanov and Zupnik. For each integer spin $s\geq 2$ we demonstrate the existence of families of conformal $\mathsf{U}(1)$ duality-invariant models, including a generalisation of the so called ModMax Electrodynamics ($s=1$). Our bosonic results are then extended to the $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetric cases. We also sketch a formalism of duality rotations for conformal gauge fields of Lorentz type $(m/2, n/2)$, for positive integers $m $ and $n$.

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arXiv2025

Anti-de Sitter flag superspace

This work aims to develop a global formulation for ${\cal N}=2$ harmonic/projective anti-de Sitter (AdS) superspace $\text{AdS}^{4|8}\times S^2 \simeq \text{AdS}^{4|8}\times {\mathbb C}P^1$ that allows for a simple action of superconformal (and hence AdS isometry) transformations. First of all, we provide an alternative supertwistor description of the ${\cal N}$-extended AdS superspace in four dimensions, AdS$^{4|4\cal N}$, which corresponds to a realisation of the connected component $\mathsf{OSp}_0({\cal N}|4; {\mathbb R})$ of the AdS isometry supergroup as $\mathsf{SU}(2,2 |{\cal N}) \bigcap \mathsf{OSp} ({\cal N}| 4; {\mathbb C})$. The proposed realisation yields the following properties: (i) AdS$^{4|4\cal N}$ is an open domain of the compactified ${\cal N}$-extended Minkowski superspace, $\overline{\mathbb M}^{4|4\cal N}$; (ii) the infinitesimal ${\cal N}$-extended superconformal transformations naturally act on AdS$^{4|4\cal N}$; and (iii) the isometry transformations of AdS$^{4|4\cal N}$ are described by those superconformal transformations which obey a certain constraint. The obtained results for AdS$^{4|4\cal N}$ are then applied to develop a supertwistor formulation for an AdS flag superspace $ \text{AdS}^{4|8} \times {\mathbb F}_1(2)$ that we identify with the ${\cal N}=2$ harmonic/projective AdS superspace. This construction makes it possible to read off the superconformal and AdS isometry transformations acting on the analytic subspace of the harmonic superspace.

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arXiv2025

Massless higher-spin supermultiplets in 5D harmonic superspace

Off-shell actions for massless higher-spin $\mathcal{N}=1$ supermultiplets in five dimensions (5D) are constructed in harmonic superspace in terms of unconstrained prepotentials. Cubic couplings of these supermultiplets to the $q$-hypermultiplet are derived. We also provide a detailed derivation of the unconstrained prepotential for the 5D Weyl supermultiplet which has been used within the conformal superspace approach to $\mathcal{N}=1$ supergravity-matter systems.

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arXiv2025

On three-dimensional ${\cal N}=4$ supersymmetry: maximally supersymmetric backgrounds and massive deformations

Using the $SO ({\cal N})$ superspace formulation for $\cal N$-extended conformal supergravity in three dimensions, we derive all maximally supersymmetric backgrounds in the ${\cal N} =4$ case. The specific feature of this choice is that the so-called super Cotton tensor $X^{IJKL} = X^{[IJKL]}$, which exists for ${\cal N} \geq 4$, is equivalent to the scalar $X$ defined by $X^{IJKL} = \varepsilon^{IJKL} X$. This scalar may be used as a deformation parameter. In the family of $(p,q)$ anti-de Sitter (AdS) superspaces with $p+q=4$, it is known that $X\neq 0$ exists only if $p=4$ and $q=0$. In general, the $(4,0)$ AdS superspaces are characterised by the structure group $SL(2,{\mathbb R}) \times SO (4)$ and their geometry is determined by two constant parameters, $S$ and $X$, of which the former determines the AdS curvature, while the $R$-symmetry curvature is determined by the parameters $(X+2S)$ and $(X-2S)$ in the left and right sectors of $SU(2)_{\rm L} \times SU(2)_{\rm R}$, respectively. Setting $S=0$ leads to the so-called deformed ${\cal N}=4$ Minkowski superspace ${\mathbb M}^{3|8}_X$ introduced thirteen years ago. We construct general interacting supersymmetric field theories in ${\mathbb M}^{3|8}_X$ and demonstrate that they originate as massive deformations of the following two families of ${\cal N} =4$ theories in standard Minkowski superspace ${\mathbb M}^{3|8}$: (i) ${\cal N}=4$ superconformal field theories; and (ii) ${\cal N}=4$ supersymmetric gauge theories in ${\mathbb M}^{3|8}$ which are not superconformal but possess the $R$-symmetry group $SU(2)_{\rm L} \times SU(2)_{\rm R}$. Extensions of the theories in (ii) to ${\mathbb M}^{3|8}_X$ necessarily contain Chern-Simons terms at the component level. We also demonstrate the generation of topologically massive ${\cal N}=4$ supersymmetric gauge theories from radiative corrections in the hypermultiplet sector.

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arXiv2025

${\mathcal N}=3$ nonlinear multiplet and supergravity

We propose an ${\mathcal N}=3$ nonlinear multiplet coupled to conformal supergravity and use it to formulate the equations of motion for ${\mathcal N} = 3$ Poincaré supergravity. These equations, which are naturally described in a new curved supergeometry with structure group $\mathsf{SL}(2,\mathbb{C})$, imply that the ${\mathcal N} = 3$ super-Bach tensor vanishes, and thus every solution of Poincaré supergravity is a solution of conformal supergravity. The aforementioned superspace formulation, which we refer to as $\mathcal N=3$ Einstein superspace, is described in terms of two dimension-$1/2$ superfields: (i) the super-Weyl spinor $W_α$; and (ii) a spinor isospinor $χ_α^i$.

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arXiv2025

Interacting $p$-form gauge theories: New developments

Gauge $p$-forms in diverse dimensions are ubiquitous in supergravity and string theory. This work reviews novel covariant formulations designed to generate arbitrary interacting duality-invariant or chiral (self-dual) $p$-form theories in $d = 2p + 2$ space-time dimensions. For odd $p$, such theories possess $\mathsf{U}(1)$ duality invariance and include the Born-Infeld and ModMax theories. For even $p$, they describe a self-interacting chiral $p$-form with its gauge-invariant field strength obeying a nonlinear self-duality condition. We provide a complete description of $T\bar T$-like deformations of $\mathsf{U}(1)$ duality-invariant models for nonlinear electrodynamics in four dimensions and their six-dimensional counterparts -- interacting chiral two-form field theories. We also elaborate on consistent flows in the spaces of duality-invariant or chiral (self-dual) $p$-form theories beyond six dimensions.

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arXiv2025

The anti-de Sitter supergeometry revisited

In a supergravity framework, the $\cal N$-extended anti-de Sitter (AdS) superspace in four spacetime dimensions, $\text{AdS}^{4|4\cal N} $, is a maximally symmetric background that is described by a curved superspace geometry with structure group $\mathsf{SL}(2, \mathbb{C}) \times \mathsf{U}({\cal N})$. On the other hand, within the group-theoretic setting, $\text{AdS}^{4|4{\cal N}} $ is realised as the coset superspace $\mathsf{OSp}({\cal N}|4;\mathbb{R}) /\big[ \mathsf{SL}(2, \mathbb{C}) \times \mathsf{O}({\cal N}) \big]$, with its structure group being $\mathsf{SL}(2, \mathbb{C}) \times \mathsf{O}({\cal N})$. Here we explain how the two frameworks are related. We give two explicit realisations of $\text{AdS}^{4|4{\cal N}} $ as a conformally flat superspace, thus extending the ${\cal N}=1$ and ${\cal N}=2$ results available in the literature. As applications, we describe: (i) a two-parameter deformation of the $\text{AdS}^{4|4{\cal N}} $ interval and the corresponding superparticle model; (ii) some implications of conformal flatness for superconformal higher-spin multiplets and an effective action generating the $\mathcal{N}=2$ super-Weyl anomaly; and (iii) $κ$-symmetry of the massless AdS superparticle.

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arXiv2025

Embedding formalism for AdS superspaces in five dimensions

The standard geometric description of $d$-dimensional anti-de Sitter (AdS) space is a quadric in ${\mathbb R}^{d-1,2}$ defined by $(X^0)^2 - (X^1)^2 - \dots - (X^{d-1})^2 + (X^d)^2 = \ell^2 = \text{const}$. In this paper we provide a supersymmetric generalisation of this embedding construction in the $d=5$ case. Specifically, a bi-supertwistor realisation is given for the ${\cal N}$-extended AdS superspace $\text{AdS}^{5|8\cal N}$, with ${\cal N}\geq 1$. The proposed formalism offers a simple construction of AdS super-invariants. As an example, we present a new model for a massive superparticle in $\text{AdS}^{5|8\cal N}$ which is manifestly invariant under the AdS isometry supergroup $\mathsf{SU}(2,2|{\cal N})$ and involves two independent two-derivative terms.

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arXiv2024

Embedding formalism for ${\mathcal N}$-extended AdS superspace in four dimensions

The supertwistor and bi-supertwistor formulations for ${\mathcal N}$-extended anti-de Sitter (AdS) superspace in four dimensions, ${\rm AdS}^{4|4\mathcal N}$, were derived two years ago in arXiv:2108.03907. In the present paper, we introduce a novel realisation of the ${\mathcal N}$-extended AdS supergroup $\mathsf{OSp}(\mathcal{N}|4;\mathbb{R})$ and apply it to develop a coset construction for ${\rm AdS}^{4|4\mathcal N}$ and the corresponding differential geometry. This realisation naturally leads to an atlas on ${\rm AdS}^{4|4\mathcal N}$ (that is a generalisation of the stereographic projection for a sphere) that consists of two charts with chiral transition functions for ${\mathcal N}>0$. A manifestly $\mathsf{OSp}(\mathcal{N}|4;\mathbb{R})$ invariant model for a superparticle in ${\rm AdS}^{4|4\mathcal N}$ is proposed. Additionally, by employing a conformal superspace approach, we describe the most general conformally flat $\mathcal N$-extended supergeometry. This construction is then specialised to the case of ${\rm AdS}^{4|4\mathcal N}$.

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arXiv2024

On equivalence of gauge-invariant models for massive integer-spin fields

There are several approaches to formulate gauge-invariant models for massive integer-spin fields in $d$ dimensions including the following: (i) in terms of symmetric tensor fields $ϕ_{μ_1 \dots μ_k} $, with $k = s, s-1, \dots , 0$, restricted to be double traceless for $k\geq 4$; and (ii) in terms of a quartet of $traceful$ symmetric tensor fields $ψ_{μ_1 \dots μ_k} $, of rank $k=s,s-1,s-2, s-3$. We demonstrate that these formulations in Minkowski space ${\mathbb M}^d$ are equivalent to the gauge-invariant theory for a massive integer-spin field proposed in 1989 by Pashnev. We also make use of the Klishevich-Zinoviev theory in ${\mathbb M}^d$ to derive a unique generalisation of the Singh-Hagen model for a massive integer-spin field in $d>4 $ dimensions.

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arXiv2024

Towards $\mathcal{N}=2$ superconformal higher-spin theory

Three years ago, we proposed free off-shell models for ${\mathcal N}=2$ superconformal higher-spin multiplets in arbitrary conformally flat backgrounds, constructed conserved conformal higher-spin supercurrents for a massless hypermultiplet, and sketched the Noether procedure to generate its cubic couplings to the superconformal higher-spin multiplets. This paper is devoted to completing the Noether procedure. Specifically, we: (i) describe the unique off-shell primary extensions of the conformal higher-spin supercurrents; (ii) embed the off-shell superconformal prepotentials into primary unconstrained isotwistor multiplets; and (iii) present the unique gauge transformations of the hypermultiplet and the isotwistor prepotentials. An extension of the Noether procedure beyond the cubic level is also sketched, following the earlier ${\mathcal N}=1$ superconformal approach developed by the authors and Ponds in 2022. Our construction is based on making use of the polar hypermultiplet within the projective-superspace setting.

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