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Evgeny Ivanov

Publications and source records attributed to Evgeny Ivanov.

At least 19 recordsLinked to original sources
arXiv2026

Casimir operators of $4D\,, \mathcal{N}=2$ supersymmetry in the harmonic approach

We construct Casimir operators of $4D, \,\mathcal{N}=2$ supersymmetry algebra in the harmonic superspace approach, and provide the explicit expressions for them in terms of covariant derivatives in the analytic basis. Specifically, the superisospin operator $C_I$ is expressed in terms of new 'long' harmonic derivatives $\nabla^{\pm\pm}, \nabla^0$ as $C_I = \frac{1}{4}\left(\nabla^0\right)^2 + \frac{1}{2}\left\{\nabla^{++},\nabla^{--}\right\}$. These derivatives involve non-local terms with the inverse Box operator $\Box^{-1}$ and satisfy modified $SU(2)$ algebra relations in which the eigenvalues of $\nabla^0$ on analytic superfields are shifted by -2 relative to the standard $U(1)$ harmonic charges. We also construct $\mathcal{N}=2$ superhelicity and super-isohelicity operators relevant to the massless case (with vanishing $\Box$) and find their eigenvalues for few instructive examples of $4D, \,\mathcal{N}=2$ superfield theories.

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arXiv2026

${\cal N}{=}\,4$ supersymmetric multiparticle systems based on indecomposable multiplets

We construct new multiparticle models of $\mathcal{N}=4$ supersymmetric mechanics with spin degrees of freedom by employing nonlinear indecomposable supermultiplets ${\bf (1,4,3){\supset\hspace{-1.1em}+}(4,4,0)}$. These systems are proper deformations of those associated with the standard irreducible $d=1$, $\mathcal{N}=4$ multiplets. In this way we find a deformation of $\mathcal{N}=4$ supersymmetric U$(2)$-spin rational Calogero system invariant under $d=1$ superconformal group OSp$(4|2)$. One more deformed model reproduces $\mathcal{N}=4$ supersymmetric U$(2)$-spin hyperbolic Calogero system, up to a shift of the Hamiltonian by some U$(1)$ generators.

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arXiv2026

Linearized $\mathcal{N}=2$ conformal supergravity in the harmonic approach

Using the harmonic superspace approach, we construct the superconformal harmonic action for $\mathcal{N}=2$ Weyl supermultiplet. The fundamental objects of the theory are unconstrained analytic potentials $h^{++α\dotα}, h^{++α+}, h^{++\dotα+}, h^{(+4)}$, which distinguishes our construction among the previously known ones. An important role is played by the ``half-analyticity'' conditions introduced in arXiv:2407.08524 [hep-th]. The structure of the harmonic linearized $\mathcal{N}=2$ Weyl action to large extent repeats the structure of the $\mathcal{N}=2$ Maxwell action, which suggests a conjecture on the possible structure of the complete nonlinear $\mathcal{N}=2$ Weyl theory action in the harmonic superspace. We provide a detailed study of the rigid superconformal properties of the proposed action and prove its invariance in both harmonic and chiral superspaces. First steps are also undertaken towards constructing the nonlinear $\mathcal{N}=2$ Weyl action, based on an analogy with $\mathcal{N}=2$ Maxwell action just mentioned and a generalization of the concept of half-analyticity to curved harmonic superspace.

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arXiv2026

Off-shell invariants of linearized $4D, \mathcal{N}=2$ supergravity in the harmonic approach

Using the harmonic superspace approach, we construct, at the linearized level, $\mathcal{N}=2$ supersymmetric curvatures generalizing scalar curvature, Ricci curvature and Weyl tensor. These supercurvatures are the building blocks of various linearized $4D, \, \mathcal{N}=2$ Einstein supergravity invariants. The supercurvatures involving the scalar and Ricci curvatures are analytic harmonic ${\cal N}=2$ superfields, while the Weyl supertensor is a chiral $\mathcal{N}=2$ superfield. As the basic distinguished feature of our construction, all these objects are expressed through the fundamental analytic gauge prepotentials $h^{++M}, M= (α\dotα, +α, +\dotα, 5)$. The related characteristic features are the heavy use of harmonic derivatives and harmonic zero-curvature equations. On a number of instructive examples, we describe the component reduction of the superfield invariants constructed.

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arXiv2026

${\cal N}=8$ supersymmetric mechanics with spin variables from indecomposable multiplets

We define two new indecomposable (not fully reducible) ${\cal N}=8$, $d=1$ off-shell multiplets and consider the corresponding models of ${\cal N}=8$ supersymmetric mechanics with spin variables. Each multiplet is described off shell by a scalar superfield which is a nonlinear deformation of the standard scalar superfield $X$ carrying the $d=1$ multiplet ${\bf (1,8,7)}$. Deformed systems involve, as invariant subsets, two different off-shell versions of the irreducible multiplet ${\bf (8,8,0)}$. For both systems we present the manifestly ${\cal N}=8$ supersymmetric superfield constraints, as well as the component off- and on-shell invariant actions, which for one version exactly match those given in arXiv:2402.00539 [hep-th]. The two models differ off shell, but prove to be equivalent to each other on shell, with the spin variables sitting in the adjoint representation of the maximal $R$-symmetry group ${\rm SO}(8)$.

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arXiv2025

${\cal N}=2$ Higher Spins by Harmonic Superspace Methods

Harmonic ${\cal N}=2$ superspace was discovered in 1984 as the powerful tool of the geometric superfield off-shell description of ${\cal N}=2, 4D$ supersymmetric field theories with the maximal spins 1, 2, and 1/2 (${\cal N}=2$ Yang-Mills theories, supergravity and matter hypermultiplets). My talk is a brief account of the basic achievements of the harmonic methods, including the newest applications in ${\cal N}=2$ theories of higher spins.

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arXiv2025

$\mathcal{N}=2$ AdS hypermultiplets in harmonic superspace

We present the harmonic superspace formulation of $\mathcal{N}=2$ hypermultiplet in AdS$_4$ background, starting from the proper realization of $4D, \mathcal{N}=2$ superconformal group $SU(2,2|2)$ on the analytic subspace coordinates. The key observation is that $\mathcal{N}=2$ AdS$_4$ supergroup $OSp(2|4)$ can be embedded as a subgroup in the superconformal group through introducing a constant symmetric matrix $c^{(ij)}$ and identifying the AdS supercharge as $Ψ^i_α= Q^i_α+ c^{ik} S_{kα}$, with $Q$ and $S$ being generators of the standard and conformal $4D, {\cal N}=2$ supersymmetries. Respectively, the AdS cosmological constant is given by the square of $c^{(ij)}$, $Λ= -12 c^{ij}c_{ij}$. We construct the $OSp(2|4)$ invariant hypermultiplet mass term by adding, to the coordinate AdS transformations, a piece realized as an extra $SO(2)$ rotation of the hypermultiplet superfield. It is analogous to the central charge $x^5$ transformation of flat $\mathcal{N}=2$ supersymmetry and turns into the latter in the super Minkowski limit. As another new result, we explicitly construct the superfield Weyl transformation to the $OSp(2|4)$ invariant AdS integration measure over the analytic superspace, which provides, in particular, a basis for unconstrained superfield formulations of the AdS$_4$-deformed $\mathcal{N}=2$ hyper Kähler sigma models. We find the proper redefinition of $θ$ coordinates ensuring the AdS-covariant form of the analytic superfield component expansions.

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arXiv2025

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

We review the superfield formulation of $\mathcal{N}=2$ higher-spin supergravity theory in harmonic superspace. The analysis of both the hypermultiplet higher-spin supersymmetries and conformal supersymmetries is performed. The analytic superspace gauging of these symmetries gives rise to a set of unconstrained analytical prepotentials describing $\mathcal{N}=2$ higher-spin off-shell supermultiplets. This procedure naturally yields cubic interaction vertices of $\mathcal{N}=2$ higher spins with the hypermultiplet. Based on these results, the consistent interaction of an infinite tower of $\mathcal{N}=2$ superconformal higher spins with hypermultiplet is presented. Proceeding from this model, a method to construct a consistent interacting theory of $\mathcal{N}=2$ higher-spin supergravity by making use of the conformal compensators is proposed.

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arXiv2025

$\mathcal{N}=2$ superconformal gravitino in harmonic superspace

We present the harmonic superspace formulation of $\mathcal{N}=2$ gravitino multiplet, the simplest $\mathcal{N}=2$ half-integer spin gauge supermultiplet. It is shown that, quite similar to other $\mathcal{N}=2$ gauge multiplets, the gravitino supermultiplet is described by unconstrained analytic prepotentials $h^{++α}$ and $h^{+++}$ which contain a conformal gravitino in the Wess-Zumino gauge. The analytic prepotentials naturally come out from the study of $\mathcal{N}=2$ supercurrents associated with hidden symmetries of $\mathcal{N}=2$ vector-hypermultiplet system. We construct the covariant $\mathcal{N}=2$ superfield strengths and the invariant $\mathcal{N}=2$ superfield actions and sketch their component contents. We observe that, at cost of introducing new auxiliary coordinates $Ψ^α$ and $ω^+$, the gravitino analytic prepotentials acquire a nice geometric interpretation as extra veilbeins of the covariant harmonic derivative $\mathfrak{D}^{++}$. We speculate on a possible origin of the additional coordinates, including their relationship with $\mathcal{N}=2$ supertwistors.

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arXiv2024

$\mathcal{N} = 2$ superconformal higher-spin multiplets and their hypermultiplet couplings

We construct an off-shell $\mathcal{N}=2$ superconformal cubic vertex for the hypermultiplet coupled to an arbitrary integer higher spin ${\bf s}$ gauge $\mathcal{N}=2$ supermultiplet % in flatfour-dimensional space. in a general $\mathcal{N}=2$ conformal supergravity background. We heavily use $\mathcal{N}=2, 4D$ harmonic superspace that provides an unconstrained superfield Lagrangian description. We start with $\mathcal{N}=2$ global superconformal symmetry transformations of the free hypermultiplet model and require invariance of the cubic vertices of general form under these transformations and their gauged version. As a result, we deduce $\mathcal{N}=2, 4D$ unconstrained analytic superconformal gauge potentials for an arbitrary integer ${\bf s}$. These are the basic ingredients of the approach under consideration. We describe the properties of the gauge potentials, derive the corresponding superconformal and gauge transformation laws, and inspect the off-shell contents of the thus obtained $\mathcal{N}=2$ superconformal higher-spin ${\bf s}$ multiplets in the Wess-Zumino gauges. The spin ${\bf s}$ multiplet involves $8(2{\bf s} -1)_B + 8(2{\bf s}-1)_F$ essential off-shell degrees of freedom. The cubic vertex has the generic structure higher spin gauge superfields $\times$ hypermultiplet supercurrents. We present the explicit form of the relevant supercurrents.

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arXiv2024

$\mathcal{N}{=}\,8$ invariant interaction of dynamical and semi-dynamical $\mathcal{N}{=}\,4$ multiplets

We present a new model of $\mathcal{N}{=}\,8$ mechanics with semi-dynamic supermultiplets. The model is constructed as an interaction of $\mathcal{N}{=}\,4$ supermultiplets which carry an implicit $\mathcal{N}{=}\,4$ supersymmetry. The initial field content consists of three dynamical $({\bf 1, 4, 3})$ multiplets: one bosonic and two fermionic. To ensure implicit $\mathcal{N}{=}\,4$ supersymmetry, we introduce the superfields describing three semi-dynamical $({\bf 4, 4, 0})$ multiplets: one fermionic and two bosonic. To avoid the second-order Lagrangian for fermions from the fermionic $({\bf 1, 4, 3})$ multiplets, the conversion of their velocities into new auxiliary fields is carried out. After conversion, these multiplets turn into semi-dynamical mirror $({\bf 4, 4, 0})$ multiplets without non-canonical terms in the $\mathcal{N}{=}\,8$ Lagrangian at the component level. The final $\mathcal{N}{=}\,8$ multiplet content is $({\bf 1, 8, 7}) \oplus ({\bf 8, 8, 0})$. As a first step to the ultimate $\mathcal{N}{=}\,4$ superfield formulation of the model, we remind a natural description of the standard and mirror $({\bf 4, 4, 0})$ multiplets in the framework of $\mathcal{N}{=}\,4, d{=}\,1$ biharmonic superspace.

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arXiv2024

$\mathcal{N}=2$ higher-spin theories and harmonic superspace

A brief review of the harmonic superspace approach to the construction of $\mathcal{N}=2$ supersymmetric higher spin theories is given. We define off-shell analytic harmonic gauge potentials of $\mathcal{N}=2$ supersymmetric higher-spin multiplets and of $\mathcal{N}=2$ superconformal higher-spin multiplets for an arbitrary integer highest spin. The component contents of these $\mathcal{N}=2$ higher-spin supermultiplets are explicitly presented. We also construct their cubic couplings to the hypermultiplet. This short report summarizes the basic results of the series of published papers [1-3] as well as announces those of the forthcoming article [4].

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arXiv2023

Non-linear (3, 4, 1) multiplet of ${\cal N} = 4$, $d = 1$ supersymmetry as a semi-dynamical spin multiplet

We consider a new type of ${\cal N}=4$, $d=1$ semi-dynamical multiplet based on the non-linear version of the mirror multiplet ${\bf (3, 4, 1)}$, with the triplet of bosonic physical fields parametrizing a three-dimensional sphere $S^3$ of the radius $R$. The limit $R\to\infty$ amounts to the contraction $S^3\to\mathbb{R}^3$ and leads to the linear mirror multiplet ${\bf (3, 4, 1)}$. Spin degrees of freedom described by a Wess-Zumino action specify a two-dimensional surface embedded in the sphere $S^3$. A pair of the examples considered correspond to the round and squashed ``fuzzy'' 2-spheres. We couple the squashed 2-sphere model to the dynamical mirror multiplet ${\bf (2, 4, 2)}$. A notable feature of this coupling is the dependence of the squashing parameter on the bosonic fields $z, \bar z$ of the chiral multiplet.

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arXiv2023

Higher Spins in Harmonic Superspace

We report on a recent progress in constructing off-shell ${\cal N}=2, 4D$ supersymmetric integer higher-spin theory in terms of unconstrained harmonic analytic gauge superfields and their cubic interaction with the matter hypermultiplets. For even superspins a new equivalent representation of the hypermultiplet couplings in terms of analytic $ω$ superfield is presented. It involves both cubic and quartic vertices.

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arXiv2023

$\mathcal{N} = 2$ higher spins: superfield equations of motion, the hypermultiplet supercurrents, and the component structure

As a continuation of our previous papers arXiv:2109.07639 and arXiv:2202.08196, we study the linearized structure of the manifestly $4D, \mathcal{N} = 2$ supersymmetric theory of the cubic couplings of the higher spin gauge superfields to the matter hypermultiplets. We consider in detail the superfield equations of motion, construct the conserved hypermultiplet superfield currents, explore their component structure (basically in the bosonic sector) and compare it with the corresponding currents in the conventional higher-spin bosonic theory. We thoroughly study the $\mathcal{N} = 2$ spin $\mathbf{2}$ and $\mathbf{3}$ models as instructive examples.

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arXiv2022

${\cal N}=2\,$ Supergravities in Harmonic Superspace

Basics of ${\cal N}=2, 4D$ conformal and Einstein supergravities in the harmonic superspace approach are outlined. The crucial merit of this formulation consists in that the relevant off-shell supermultiplets, in particular ${\cal N}=2, 4D$ superconformal Weyl multiplet, are accommodated by the harmonic-analytic unconstrained prepotentials with a clear geometric meaning, like in the analogous formulation of ${\cal N}=2, 4D$ supersymmetric gauge theory. The fundamental gauge group of conformal supergravity is constituted by the analyticity-preserving diffeomorphisms of harmonic superspace. The superfield actions of various off-shell versions of ${\cal N}=2$ Einstein supergravity are obtained as the actions of the appropriate harmonic analytic compensators in the background of conformal ${\cal N}=2$ supergravity. The version admitting the most general couplings to quaternion-Kähler matter is the ``principal'' version with the unconstrained harmonic analytic hypermultiplet superfield as a compensator. It involves an infinite number of auxiliary fields.

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arXiv2022

Off-shell cubic hypermultiplet couplings to $\mathcal{N}=2$ higher spin gauge superfields

We construct manifestly $4D, \mathcal{N}=2$ supersymmetric and gauge invariant off-shell cubic couplings of matter hypermultiplets to the higher integer spin gauge $\mathcal{N}=2$ multiplets introduced in arXiv:2109.07639 [hep-th]. The hypermultiplet is described by an analytic harmonic $4D, \mathcal{N}=2$ superfield $q^{+}$ with the physical component spins ${\bf s} = (\frac{1}{2}\,, \;0)$ and an infinite number of auxiliary fields. The cubic coupling constructed has the schematic structure $q^+ \hat{\cal H}^{++}_{(s)} q^+$, where $\hat{\cal H}^{++}_{(s)}$ is a differential analytic operator of the highest degree $({\bf s} - 1)$ accommodating the massless gauge $\mathcal{N}=2$ multiplet with the highest spin ${\bf s}$. For odd ${\bf s}$ the gauge group generators and couplings are proportional to ${\rm U}(1)_{PG}$ generator of the internal ${\rm SU}(2)_{PG}$ symmetry of the hypermultiplet and so do not exist if ${\rm SU}(2)_{PG}$ is unbroken. If this ${\rm U}(1)_{PG}$ is identified with the central charge of $ 4D, \mathcal{N}=2$ supersymmetry, a mass for the hypermultiplet is generated and the odd ${\bf s}$ couplings vanish in the proper massless limit. For even ${\bf s}$ the higher-spin gauge transformations and cubic superfield couplings can be defined for both massive and massless (central-charge neutral) hypermultiplets without including ${\rm U}(1)_{PG}$ generator. All these features directly extend to the case of $n$ hypermultiplets with the maximal internal symmetry ${\rm USp}(2n) \times {\rm SU}(2)$.

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