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A. V. Korybut

Publications and source records attributed to A. V. Korybut.

15 recordsLinked to original sources
arXiv2026

Gauge transformations in Z-space in (anti)holomorphic sector of HS theory

We consider a consistent deformation of the (anti)holomorphic generating system of [arXiv:2209.01966], aiming to provide a map to the (anti)holomorphic truncation of the Vasiliev theory. In our new formulation, the previously rigidly defined master-field $Λ$ can be shifted by $\mathrm{d}_z$-exact projective one-forms. The class of projective one-forms is described comprehensively, and corresponding projective identities are proven. $\mathrm{d}_z$-exact forms of the order $n$ in $C$ induce field redefinition of order $(n+1)$ and beyond. Explicit expression for the $(n+1)$-th order field redefinitions are provided. An analysis of the gauge transformation of the second order in $C$ in zero-forms is performed, identifying necessary and sufficient conditions for the part of the field redefinition of the second order that can be gauged away. The field redefinitions induced by the shift of $Λ$ are proven to be nontrivial.

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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 $-2\leqλ\leq 0$ 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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arXiv2025

On consistency of the interacting (anti)holomorphic higher-spin sector

In the recently proposed generating systems for the (anti)holomorphic sector of the 4d higher spin theory and for the off-shell higher spin theory in generic dimension locality was achieved due to a peculiar limiting star product. Even though the generating systems exhibit all-order locality, the product itself encounters uncertainties when functions from specific classes are multiplied. This fact leads to the absence of the Leibniz rule for the differential operator acting on the auxiliary variables $z$ and, hence, its ambiguous definition in the generating equations. We identify the gap in the original proof of consistency associated with this freedom. Nonetheless considered generating systems are perfectly consistent as shown by direct computations on the resulting vertices. Considering specific orderings of fields we show that consistency rests on the star-exchange-like identities for the limiting star product formulated and proved here. Connection with the 4d Vasiliev theory is discussed.

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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

Disentanglement of Topological and Dynamical Fields in 3d Higher-Spin Theory within Shifted Homotopy Approach

The first-order correction to the one-form sector of equations of the $3d$ higher-spin theory is derived from the generating nonlinear HS system by virtue of the shifted homotopy approach. The family of solutions to the generating system that disentangles equations for dynamical and topological fields in the first order of perturbation theory is found. This family is shown to belong to the different cohomology class compared to the solution found earlier by the direct methods. The related cohomology is shown to be the same as that underlying the mass deformation in the matter sector of $3d$ higher-spin equations.

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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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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

Manifest Form of the Spin-Local Higher-Spin Vertex $Υ^{ηη}_{ωCCC}$

Vasiliev generating system of higher-spin equations allowing to reconstruct nonlinear vertices of field equations for higher-spin gauge fields contains a free complex parameter $η$. Solving the generating system order by order one obtains physical vertices proportional to various powers of $η$ and $\barη$. Recently $η^2$ and $\barη^2$ vertices in the zero-form sector were presented in 2009.02811 in the $Z$-dominated form implying their spin-locality by virtue of $Z$-dominance Lemma of 1805.11941. However the vertex of 2009.02811 had the form of a sum of spin-local terms dependent on the auxiliary spinor variable $Z$ in the theory modulo so-called $Z$-dominated terms, providing a sort of existence theorem rather than explicit form of the vertex. The aim of this paper is to elaborate an approach allowing to systematically account for the effect of $Z$-dominated terms on the final $Z$-independent form of the vertex needed for any practical analysis. Namely, in this paper we obtain explicit $Z$-independent spin-local form for the vertex $Υ^{ηη}_{ωCCC}$ for its $ωCCC$-ordered part where $ω$ and $C$ denote gauge one-form and field strength zero-form higher-spin fields valued in an arbitrary associative algebra in which case the order of product factors in the vertex matters. The developed formalism is based on the Generalized Triangle identity derived in the paper and is applicable to all other orderings of the fields in the vertex.

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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.

hep-th↗
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

Star product for deformed oscillator algebra $\mathsf{Aq}(2,ν)$

An analogue of the Moyal star product is presented for the deformed oscillator algebra. It contains several homotopy-like additional integration parameters in the multiplication kernel generalizing the differential Moyal star-product formula $\exp[iε_{αβ}\partial^α\partial^β]$. Using Pochhammer formula, integration over these parameters is carried over a Riemann surface associated with the expression of the type $z^x (1-z)^y$ where $x$ and $y$ are arbitrary real numbers.

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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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