arXiv subjects

V. E. Didenko

Publications and source records attributed to V. E. Didenko.

At least 19 recordsLinked to original sources

arXiv2026

Classifying double copies and multicopies in AdS

In this paper, we draw a parallel between solutions of pure three-dimensional gravity with a negative cosmological constant and classical double copies in four dimensions. In the former case, topological solutions, such as the BTZ black hole, deficit angles, and naked singularities, emerge from identifying points in AdS using elements from its isometry algebra $so(2,2)$. The type of solution corresponds one-to-one with the orbits of $so(2,2)$. We demonstrate how various double copies of four-dimensional AdS gravity similarly arise from the $so(2,3)$ isometry elements, which also correspond one-to-one with their orbits through a Penrose-type transform. We classify all such elements and generate the corresponding double copies, which include AdS black holes, black branes, and many others. The double-copy isometries originate from the centralizer of a given AdS isometry, allowing us to define canonical coordinates associated with its Abelian part. Additionally, the two Casimir invariants of $so(2,3)$ feature in the metrics. Our classification naturally extends to higher spins, providing nonequivalent multicopies at the linearized level.

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arXiv2026

Self-dual gravity from higher-spin theory

Higher-spin symmetry is known to mix lower-spin fields with higher-spin fields, creating a complex interaction picture where no closed finite field sector is expected to exist for dimensions greater than three. By studying the self-dual part of higher-spin interaction vertices in four dimensions, we show that gauge fields of spins greater than two can be consistently set to zero. In this case, the fields with helicities $-2\leq\lambda\leq 0$ form a closed sub-sector and also act as sources for positive helicities. For these lower spin fields, we identify their equations of motion. In particular, we show that self-dual gravity with a cosmological constant emerges as a unique rigid part of higher-spin interactions. Notably, its equations have a form that incorporates the Moyal star product, which is essential for generating the higher-spin algebra. Therefore, we demonstrate that self-dual gravity can be derived from higher-spin symmetries.

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arXiv2026

Irregular higher-spin generating equations and chiral perturbation theory

We present a complementary approach to the standard Vasiliev framework for nonlinear higher-spin interactions in four dimensions, aimed at identifying their minimally nonlocal form. Our proposal introduces a generating system for higher-spin vertices at the level of classical equations, which we refer to as irregular, in contrast to the regular case described by Vasiliev. This system extends the recently proposed equations for (anti)holomorphic interactions by incorporating the mixed sector. Its perturbative series encompasses the entire (anti)holomorphic sector in the leading order, with vertices related to powers of the complex parity-breaking parameter $\eta$ or $\bar\eta$. The subsequent corrections facilitate the mixing of the two sectors, with vertices carrying mixed powers of $\eta$ and $\bar\eta$. The consistency relies on the nonlinear algebraic constraint, which is shown to be satisfied at least in the quadratic and cubic approximations. As a result, the previously discussed (anti)holomorphic interactions in the literature can be systematically extended to generate vertices of the form $\eta^N \bar\eta^k$ and their conjugate, at least for $k \leq 2$ and any $N$. As a byproduct of our analysis, we also identify the new higher-spin structure dualities.

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arXiv2025

On symmetry breaking in the self-dual higher-spin theory

We explore the symmetry-broken phase of the self-dual (chiral) sector of higher-spin theory in four dimensions. To that end, we construct a two-parameter vacuum that breaks the AdS symmetry but remains symmetric under the leftover Poincar\'{e} algebra in three dimensions. The vacuum non-zero fields include spin-two AdS frame fields and a scalar, which has a profile that extends along the AdS radial direction. The two free parameters correspond to two scalar branches of conformal dimensions $\Delta=1$ and $\Delta=2$. Focusing on the $\Delta=1$ branch, we analyze the dynamics of free fields around this vacuum and examine its holographic dual. We observe that certain higher spin states decouple in the broken phase. This is illustrated by a set of gauge fluctuations, which acquire no source from higher-spin currents, leading to their complete decoupling, except for the gauge field associated with spin one. The dual higher-spin currents appear to be disentangled from the gauge fields and generally do not conserve; however, their lower-spin components with helicities $s = -1, 0$, and $\pm 1/2$ remain unaffected by the symmetry breaking. Notably, the helicity $s=+1$ current, while deformed, remains conserved.

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arXiv2024

All vertices for unconstrained symmetric gauge fields

Recently, the generating system that describes interacting symmetric higher-spin gauge fields at the level of equations of motion was proposed. The interaction vertices it offers are 'off the mass shell' unless constrained by the prescribed factorization condition that properly removes traceful components. In this paper we detail the structure of the unconstrained, i.e., traceful vertices. We derive their manifest form to all orders along with a net of the associated dualities, thus providing the complete higher-spin vertex analysis at the unconstrained level for the bosonic theory in any dimension. These vertices are shown to be the minimal space-time local and have a form of the peculiar integrals over a space of closed polygons, which we scrutinize in the paper. The obtained results directly apply to the holomorphic sector of the four-dimensional theory, where the interaction is on shell, producing the all-order chiral higher-spin vertices.

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arXiv2024

Toward higher-spin symmetry breaking in the bulk

We present a new vacuum of the bosonic higher-spin gauge theory in $d+1$ dimensions, which has leftover symmetry of the Poincaré algebra in $d$ dimensions. Its structure is very simple: the space-time geometry is that of $AdS$, while the only nonzero field is a scalar. The scalar extends along the Poincaré radial coordinate $z$ and is shown to be linearly exact for an arbitrary mixture of its two $Δ=2$ and $Δ=d-2$ conformal branches. The obtained vacuum breaks the global higher-spin symmetry leading to a broken phase that lives in the Minkowski space-time.

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arXiv2024

Interaction of symmetric higher-spin gauge fields

We show that the recently proposed equations for holomorphic sector of higher-spin theory in $d=4$, also known as chiral, can be naturally extended to describe interacting symmetric higher-spin gauge fields in any dimension. This is achieved with the aid of Vasiliev's off shell higher-spin algebra. The latter contains ideal associated to traces that has to be factored out in order to set the equations on shell. To identify the ideal in interactions we observe the global $sp(2)$ that underlies it to all orders. The $sp(2)$ field dependent generators are found in closed form and appear to be remarkably simple. The traceful higher-spin vertices are analyzed against locality and shown to be all-order space-time spin-local in the gauge sector, as well as spin-local in the Weyl sector. The vertices are found manifestly in the form of curious integrals over hypersimplices. We also extend to any $d$ the earlier observed in $d=4$ higher-spin shift symmetry known to be tightly related to spin-locality.

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arXiv2023

Classical double copy and higher-spin fields

Kerr-Schild double copy is shown to extend naturally to all free symmetric gauge fields propagating on $(A)dS$ in any dimension. Similarly to the standard lower-spin case, the higher-spin multicopy comes along with the zeroth, single, and double copies. The mass-like term of the Fronsdal spin $s$ field equations fixed by gauge symmetry and the mass of the zeroth copy both appear to be remarkably fine-tuned to fit the multicopy pattern forming a spectrum organized by higher-spin symmetry. On the black hole side this curious observation fills up the list of miraculous properties of the Kerr solution.

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arXiv2022

On $z$-dominance, shift symmetry and spin locality in higher-spin theory

The paper aims at the qualitative criterion of higher-spin locality. Perturbative analysis of the Vasiliev equations gives rise to the so-called $z$-dominated non-localities which nevertheless disappear from interaction vertices leaving the final result spin-local in all known cases. This has led one to the $z$ -- dominance conjecture that suggests universality of the observed cancellations. Here we specify conditions which include observation of the higher-spin shift symmetry and prove validity of this recently proposed conjecture. We also define a class of spin-local and shift-symmetric field redefinitions which is argued to be the admissible one with respect to spin-locality.

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arXiv2022

On holomorphic sector of higher-spin theory

Recent investigation of locality problem for higher-spin fields led to a vertex reconstruction procedure that involved elements of contraction of the original Vasiliev interaction algebra. Inspired by these results we propose the Vasiliev-like generating equations for holomorphic higher-spin interactions in four dimensions based on the observed contracted algebra. We specify the functional class that admits evolution on the proposed equations and brings in a systematic procedure of extracting all-order holomorphic vertices. A simple consequence of the proposed equations is space-time locality of the gauge field sector. We also show that vertices come with a remarkable shift symmetry.

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arXiv2021

Planar solutions of higher-spin theory. Nonlinear corrections

Leading order higher-spin corrections to the linearized higher-spin black brane are analyzed in four dimensions. It is shown that the static solution that respects planar symmetry exists in the bosonic case at given order. Its higher-spin Weyl tensors are found in a closed form and are shown to have the double copy origin. The effect of higher-spin fields to form a strictly positive scalar condensate for any values of higher-spin charges is observed.

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arXiv2021

Planar solutions of higher-spin theory I: free field level

Many black hole solutions of General Relativity are known to be linearly exact. This opens a way to study them in gauge theories that apart from gravity contain fields of higher spin $s>2$. Starting with a black brane in $AdS_4$ we find its free field higher-spin generalization that respects static and planar symmetry for all bosonic gauge fields $s\geq 0$. The solution is found for both the higher-spin curvatures and potentials in the form suitable for further non-linear analysis and satisfies the multi copy relation.

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arXiv2021

Spin-Locality of $η^2$ and $\barη^2$ Quartic Higher-Spin Vertices

Higher-spin theory contains a complex coupling parameter $η$. Different higher-spin vertices are associated with different powers of $η$ and its complex conjugate $\bar η$. Using $Z$-dominance Lemma, that controls spin-locality of the higher-spin equations, we show that the third-order contribution to the zero-form $B(Z;Y;K)$ admits a $Z$-dominated form that leads to spin-local vertices in the $η^2$ and $\bar η^2$ sectors of the higher-spin equations. These vertices include, in particular, the $η^2$ and $\bar η^2$ parts of the $ϕ^4$ scalar field vertex.

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arXiv2021

Homotopy Properties and Lower-Order Vertices in Higher-Spin Equations

New homotopy approach to the analysis of nonlinear higher-spin equations is developed. It is shown to directly reproduce the previously obtained local vertices. Simplest cubic (quartic in Lagrangian nomenclature) higher-spin interaction vertices in four dimensional theory are examined from locality perspective by the new approach and shown to be local. The results are obtained in a background independent fashion.

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arXiv2020

Limiting Shifted Homotopy in Higher-Spin Theory and Spin-Locality

Higher-spin vertices containing up to quintic interactions at the Lagrangian level are explicitly calculated in the one-form sector of the non-linear unfolded higher-spin equations using a $β\to-\infty$--shifted contracting homotopy introduced in the paper. The problem is solved in a background independent way and for any value of the complex parameter $η$ in the HS equations. All obtained vertices are shown to be spin-local containing a finite number of derivatives in the spinor space for any given set of spins. The vertices proportional to $η^2$ and $\bar η^2$ are in addition ultra-local, i.e. zero-forms that enter into the vertex in question are free from the dependence on at least one of the spinor variables $y$ or $\bar y$. Also the $η^2$ and $\bar η^2$ vertices are shown to vanish on any purely gravitational background hence not contributing to the higher-spin current interactions on $AdS_4$. This implies in particular that the gravitational constant in front of the stress tensor is positive being proportional to $η\bar η$. It is shown that the $β$-shifted homotopy technique developed in this paper can be reinterpreted as the conventional one but in the $β$-dependent deformed star product.

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arXiv2019

Exact higher-spin symmetry in CFT: free fermion correlators from Vasiliev Theory

N-point correlation functions of conserved currents and weight-two scalar operators of the three-dimensional free fermion vector model are found as invariants of the higher-spin symmetry in four-dimensional AdS. These are the correlators of the unbroken Vasiliev higher-spin theory. The results extend the recent work arXiv:1210.7963 and are complementary to arXiv:1301.3123 where the correlators were computed entirely on the boundary.

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arXiv2018

Lorentz covariant form of extended higher-spin equations

The extension of nonlinear higher-spin equations in d=4 proposed in [arXiv:1504.07289] for the construction of invariant functional is shown to respect local Lorentz symmetry. The equations are rewritten in a manifestly Lorentz covariant form resulting from some Stueckelberg-like field transformation. We also show that the two field-independent central terms entering higher-spin equations which are not entirely fixed by the consistency alone get fixed unambiguously by the requirement of Lorentz symmetry. One of the important advantages of the proposed approach demonstrated in the paper is the remarkable simplification of the perturbative analysis.

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arXiv2017

Test of the local form of higher-spin equations via AdS/CFT

The local form of higher-spin equations found recently to the second order [1] is shown to properly reproduce the anticipated $AdS/CFT$ correlators for appropriate boundary conditions. It is argued that consistent $AdS/CFT$ holography for the parity-broken boundary models needs a nontrivial modification of the bosonic truncation of the original higher-spin theory with the doubled number of fields, as well as a nonlinear deformation of the boundary conditions in the higher orders.

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