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Nikita Zaigraev

Publications and source records attributed to Nikita Zaigraev.

16 recordsLinked to original sources
arXiv2026

Structure of $\mathcal{N} = 2$ superfield higher-spin abelian cubic interactions

In this article we study the structure of the $\mathcal{N}=2$ abelian higher-spin cubic $(\mathbf{s_1}, \mathbf{s_2}, \mathbf{s_2})$ vertices and the corresponding $\mathcal{N}=2$ higher-spin supercurrents, introduced in arXiv:2408.00668. These interactions are possible only for $\mathbf{s_1} \geq 2 \mathbf{s_2}$. Conserved supercurrents are constructed as descendants of the \textit{principal supercurrent}, which is uniquely characterized by simple differential conditions and admits an explicit representation in terms of $\mathcal{N}=2$ higher-spin super-Weyl tensors. We derive the analytic form of the abelian vertices and identify the corresponding analytic higher-spin $\mathcal{N}=2$ supercurrents. We show that the vertex structure is fully determined by the analytic supercurrents $J^{++}_{α(s-1)\dotα(s-1)}$, $J^+_{α(s-1)\dotα(s-2)}$, and $\bar{J}^+_{α(s-2)\dotα(s-1)}$. The analytic form of the vertices provides a simple framework for analyzing their component structure. As an example, we explore the component content of such interactions on the Bel--Robinson diagonal. Using the superfield inverse Noether procedure, we study higher-spin gauge transformations for the $\mathcal{N}=2$ vector multiplet associated with the $(\mathbf{s}, \mathbf{1}, \mathbf{1})$ interaction. In the rigid limit, for odd $\mathbf{s}$ these transformations reduce to the $\mathcal{N}=2$ superspace generalization of zilch-type higher-spin symmetries.

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arXiv2026

Wess-Zumino gauge for analytic prepotentials of off-shell $\mathcal{N}=2$ supergravity: bosonic sector

We present a comprehensive study of the Wess-Zumino gauge for the analytic prepotentials of the off-shell $\mathcal{N}=2$ Weyl and $\mathcal{N}=2$ Einstein supergravities (the version with a non-linear tensor compensator). The field redefinitions, the full transformation laws, and the gauge superparameters that preserve the Wess-Zumino gauge are derived. As a concrete application of the obtained results, we examine the component structure of the free hypermultiplet action coupled to $\mathcal{N}=2$ supergravity. In this work, we restrict our analysis strictly to the bosonic sector.

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arXiv2026

Novel $\mathcal{N}=2$ higher-spin supercurrents

We study cubic interactions of $\mathcal N=2$ massless integer-spin gauge supermultiplets in harmonic superspace. We construct the complete class of abelian $(\mathbf{s},\mathbf{s_1},\mathbf{s_2})$ cubic vertices with the minimal number of space-time derivatives. Such vertices exist only for $\mathbf{s}\geq \mathbf{s_1}+\mathbf{s_2}$ and universally take the form of the gauge prepotential coupled to the conserved higher-spin supercurrent. For~$\mathbf{s_1}\neq\mathbf{s_2}$, we find the novel complex principal supercurrent, whose real and imaginary parts generate the parity-invariant and the parity-breaking interactions, respectively. The supercurrents are constructed from gauge-invariant $\mathcal N=2$ higher-spin Weyl supertensors associated with the spin-$\mathbf{s_1}$ and spin-$\mathbf{s_2}$ gauge multiplets. These supertensors are defined in terms of unconstrained higher-spin analytic prepotentials. We also derive the complete set of conserved component higher-spin currents associated with the $(s,s_1,s_2)$ vertices, including both traceless currents and currents with the non-vanishing trace.

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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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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

$\mathcal{N}=2$ higher-spin supercurrents

We have constructed conserved $\mathcal{N}=2$ higher-spin supercurrents for an arbitrary integer spin through the unconstrained superfield formulation of $4D,\, \mathcal{N}=2$ massless higher-spin theories in the harmonic superspace. The obtained supercurrents are gauge-invariant and determine consistent cubic interactions in the \textit{gauge superfield} $\times$ \textit{supercurrent} form for massless spin $\mathbf{s_1}$ and two massless spin $\mathbf{s_2}$ $\mathcal{N}=2$ supermultiplets. Such interactions and $\mathcal{N}=2$ supercurrents exist only for $\mathbf{s_1}\geq 2 \mathbf{s_2}$. These supercurrents are the $\mathcal{N}=2$ supersymmetric extension of Berends-Burgers-van Dam higher-spin currents and generalize the linearized Bel-Robinson tensor. The relevant $\mathcal{N}=2$ supercurrents can be considered as the descendants of the $\mathcal{N}=2$ principle supercurrent, which has a simple universal structure. An important feature of our outcomes is that, ultimately, all $\mathcal{N}=2$ supercurrents are built from the $\mathcal{N}=2$ superfield strengths, which are constructed from the unconstrained analytical higher-spin prepotentials.

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arXiv2024

Vacuum Condensates on the Coulomb Branch

We study correlation functions on the Coulomb branch of planar $\mathcal{N} = 4$ super-Yang- Mills theory (SYM), and their relationship with integrability, the operator product expansion (OPE), the sum rule, the large charge expansion, and holography. First, we compute one-point functions of arbitrary scalar operators at weak coupling and derive a compact spin-chain representation. We next study the two-point functions of chiral primaries at one loop and find that the radius of convergence of OPE in position space is infinite. We estimate the asymptotic growth of the OPE data based on this finding. Finally, we propose a concrete nonperturbative formula that connects the correlation functions on the Coulomb branch with the correlation functions with large charge insertions at the conformal point and provide a holographic interpretation based on a large D3-brane in AdS. The formula extends the known connection between the large charge sector and the Coulomb branch for rank-1 theories to the large $N$ limit.

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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

$\mathcal{N}=2$ 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

$\mathcal{N} = 2$ 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

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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arXiv2021

Unconstrained off-shell superfield formulation of $4D, \mathcal{N}=2$ supersymmetric higher spins

We present, for the first time, the complete off-shell $4D, {\cal N}=2$ superfield actions for any free massless integer spin ${\bf s} \geq 2$ fields, using the ${\cal N}=2$ harmonic superspace approach. The relevant gauge supermultiplet is accommodated by two real analytic bosonic superfields $h^{++}_{α(s-1)\dotα(s-1)}$, $h^{++}_{α(s-2)\dotα(s-2)}$ and two conjugated complex analytic spinor superfields $h^{+3}_{α(s-1)\dotα(s-2)}$, $h^{+3}_{α(s-2)\dotα(s-1)}\,$, where $α(s) := (α_1\ldots α_s), \dotα(s) := (\dotα_1\ldots \dotα_s)$. Like in the harmonic superspace formulations of ${\cal N}=2$ Maxwell and supergravity theories, an infinite number of original off-shell degrees of freedom is reduced to the finite set (in WZ-type gauge) due to an infinite number of the component gauge parameters in the analytic superfield parameters. On shell, the standard spin content $({\bf s, s-1/2, s-1/2, s-1})$ is restored. For ${\bf s}=2$ the action describes the linearized version of "minimal" ${\cal N}=2$ Einstein supergravity.

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