arXiv subjects

M. A. Vasiliev

Publications and source records attributed to M. A. Vasiliev.

At least 19 recordsLinked to original sources

arXiv2026

Differential Contracting Homotopy in the Linearized 3d Higher-Spin Theory

In this paper, the recently developed differential homotopy approach is applied to the problem of disentangling dynamical and topological fields of the $3d$ higher-spin gauge theory at the linear level. This formalism allows us to reproduce all known disentangling solutions in a unified form, including both the solutions obtained previously within the shifted homotopy approach in \cite{Korybut:2022kdx} and that derived by hand in \cite{Vasiliev:1992ix}, as well as other solutions including those associated with the cohomology of the background covariant derivative $D_0$. Also, within the differential homotopy framework an alternative way of derivation of disentangled equations through a non-conventional solution for the field $S_1$ is suggested. The obtained results are important for further analysis of nonlinear corrections to HS equations in $AdS_3$.

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arXiv2026

Quadratic Corrections to the Higher-Spin Equations by the Differential Homotopy Approach

The recently proposed differential homotopy approach to the analysis of nonlinear higher spin theory is developed. The Ansatz is extended to the form applicable in the second order of the perturbation theory and general star-multiplication formulae are derived. The relation of the shifted homotopy and differential homotopy formalisms is worked out. Projectively-compact spin-local quadratic (anti)holomorphic vertices in the one-form sector of higher-spin equations are obtained within the differential homotopy formalism.

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arXiv2025

Lorentz Covariance of the $4d$ Nonlinear Higher-Spin Equations via BRST

We propose a BRST extension of the higher-spin gauge theory in $AdS_4$ with the BRST operator associated with the local Lorentz symmetry. Our construction supports manifest local Lorentz covariance and is applicable both to any homotopy scheme of the perturbative analysis including the recently proposed differential homotopy and to the variety of further extended higher-spin models in $AdS_3$ and $AdS_4$ with higher differential forms and Coxeter higher-spin algebras.

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arXiv2025

Linearized Coxeter Higher-Spin Theories

A class of higher-spin gauge theories on $AdS_4$ associated with various Coxeter groups $\mathcal{C}$ is analyzed at the linear order. For a general $\mathcal{C}$, a solution corresponding to the $AdS_4$ space and the form of the free unfolded equations are established. A disentanglement criterion has been formulated for Coxeter HS modules. The shifted homotopy technique is uplifted to the general Coxeter HS models. In case of the Coxeter group $B_2$ classification of unitary HS modules and a consistent truncation to them are determined, the dynamical content is discussed briefly.

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arXiv2025

Supersymmetric Higher-Spin Gauge Theories in any $d$ and their Coupling Constants within BRST Formalism

Nonlinear field equations for the supersymmetric higher-spin gauge theory describing totally symmetric bosonic and fermionic massless fields along with hook-type bosonic fields of all spins in any space-time dimension are presented. One of the novel features of the proposed formalism is that the $osp(1,2)$ invariance and factorisation conditions are formulated within the BRST formalism, that greatly simplifies the form of nonlinear HS equations. To match the list of vertices found by Metsaev, higher-spin gauge theory is anticipated to possess an infinite number of independent coupling constants. A conjecture that these coupling constants result from the locality restrictions on the elements of the factorisation ideal is put forward.

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arXiv2025

Dirac Singleton as a Relativistic Field Beyond Standard Model

A new interpretation of Dirac singletons \cite{Dirac:1963ta}, i.e. free conformal fields in $d$ dimensions, as relativistic fields in a $d+1$-dimensional space-time with cosmological constant, that differs from the Flato-Fronsdal dipole construction in $AdS_{d+1}$ \cite{Flato:1986uh}, is proposed. The $d+1$-dimensional field is described at the level of both equations and Lagrangian. It forms an infinite-dimensional representation of the $d+1$-dimensional Lorentz group that relates fields at different space-time points. The associated well-known fact is that singleton cannot be localized at a point in ${d+1}$ dimensions, hence being unobservable via local scattering/radiation phenomena in the Standard Model ($d=3$). On the other hand, that singleton respects ${d+1}$ dimensional relativistic symmetries makes it possible to introduce its interactions with gravity and other relativistic fields in $d+1$ dimensions. It is speculated that the presence of singleton in a four-dimensional field theory with non-zero cosmological constant (dark energy) can be relevant to the dark matter phenomenon and baryon asymmetry generation.

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arXiv2024

Bilinear Fronsdal currents in the $AdS_{4}$ higher-spin theory

We analyse higher-spin theory with general coupling constant $η$ at the second order, focusing on the gauge non-invariant vertices $Υ(ω,ω)$, $Υ(Ω,ω,C)$ and $Υ(ω,C)$, that are shown to generate nontrivial currents in the Fronsdal equations. Explicit expressions for the currents are found in the frame-like formalism counterpart of the TT gauge worked out in the paper. The nonlinear higher-spin theory is shown to generate all types of Metsaev's currents with the coupling constants manifestly expressed via the complex coupling constant $η$ of the higher-spin theory. It is shown that all currents in the higher-spin theory are conformal in the TT gauge except for those bilinear in the higher-spin gauge fields $ω$.

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arXiv2024

The $σ_-$ Cohomology Analysis for Symmetric Higher-Spin Fields

In this paper, we present a complete proof of the so-called First On-Shell Theorem that determines dynamical content of the unfolded equations for free symmetric massless fields of arbitrary integer spin in any dimension and arbitrary integer or half-integer spin in four dimensions. This is achieved by calculation of the respective $σ_-$ cohomology both in the tensor language in Minkowski space of any dimension and in terms of spinors in $AdS_4$. In the $d$-dimensional case $H^p(σ_-)$ is computed for any $p$ and interpretation of $H^p(σ_-)$ is given both for the original Fronsdal system and for the associated systems of higher form fields.

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arXiv2024

Gauge Non-Invariant Higher-Spin Currents in $AdS_4$

Conserved currents of any spin $t>0$ built from bosonic symmetric massless gauge fields of arbitrary integer spins in $AdS_4$ are found. Analogously to the case of $4d$ Minkowski space, currents considered in this paper are not gauge invariant but generate gauge invariant conserved charges.

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arXiv2024

Off-Shell Fields and Conserved Currents

We study interactions of higher-spin massless fields $φ$ with conserved currents multilinear in the off-shell matter fields $ϕ$. Specifically, we focus on the 3d case where a slight modification of the $σ_-$-cohomology technique developed earlier is directly applicable to control nontriviality of the interaction vertices at the convention that the vertices removable by a local field redefinition of a higher-spin field or having schematic form $F(φ) G(ϕ)$, where $F(φ)$ is a gauge invariant field strength of a free higher-spin field, are called deformationally trivial. It is demonstrated how the $σ_-$-cohomology approach can be applied to the analysis of nonlinear vertices. Generally, deformationally trivial vertices are not $σ_-$-closed while the deformationally non-trivial ones must be in $H(σ_-)$. It is shown that, at least in the $3d$ case, the relevant cohomology group $H^1(σ_-)=0$ and, hence, no deformationally non-trivial off-shell vertices exist. On the other hand, there exists an infinite class of deformationally trivial vertices, that includes the vertex recently proposed for spin three. Our analysis goes beyond the higher-spin vertices allowing to show that, at least in three dimensions, nonlinear combinations of the off-shell scalar fields and their derivatives cannot obey non-trivial equations.

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arXiv2023

Differential Contracting Homotopy in Higher-Spin Theory

A new efficient approach to the analysis of nonlinear higher-spin equations, that treats democratically auxiliary spinor variables $Z_A$ and integration homotopy parameters in the non-linear vertices of the higher-spin theory, is developed. Being most general, the proposed approach is the same time far simpler than those available so far. In particular, it is free from the necessity to use the Schouten identity. Remarkably, the problem of reconstruction of higher-spin vertices is mapped to certain polyhedra cohomology in terms of homotopy parameters themselves. The new scheme provides a powerful tool for the study of higher-order corrections in higher-spin theory and, in particular, its spin-locality. It is illustrated by the analysis of the lower order vertices, reproducing not only the results obtained previously by the shifted homotopy approach but also projectively-compact vertices with the minimal number of derivatives, that were so far unreachable within that scheme.

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arXiv2023

Shifted Homotopy Analysis of the Linearized Higher-Spin Equations in Arbitrary Higher-Spin Background

Analysis of the first-order corrections to higher-spin equations is extended to homotopy operators involving shift parameters with respect to the spinor $Y$ variables, the argument of the higher-spin connection $ω(Y)$ and the argument of the higher-spin zero-form $C(Y)$. It is shown that a relaxed uniform $(y+p)$-shift and a shift by the argument of $ω(Y)$ respect the proper form of the free higher-spin equations and constitute a one-parametric class of vertices that contains those resulting from the conventional (no shift) homotopy. A pure shift by the argument of $ω(Y)$ is shown not to affect the one-form higher-spin field $W$ in the first order and, hence, the form of the respective vertices.

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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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arXiv2023

Unfolded Point Particle as a Field in Minkowski Space

Point-particle dynamics is reformulated as a field theory. This is achieved by using the unfolded dynamics approach that makes it possible to give dynamical interpretation to the concept of physical dimension which is 1 for a point particle in the $d$-dimensional space-time. The main idea for the description of a $k$-dimensional on-shell system in the $d$-dimensional space is to keep the evolution along $d-k$ dimensions off-shell or, alternatively, restrict it in a specific way respecting the compatibility conditions of the resulting unfolded system. The developed approach gives some hints how a non-linear realization of the symmetry $G$ of a larger-dimensional space in a lower-dimensional system can emerge from a geometrical realization on the fields in an appropriate $G$-invariant space. For the example of a relativistic point particle considered in this paper, $ G$ is the Poincare group. The proposed general scheme is illustrated by simple examples that reproduce conventional results.

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arXiv2022

Projectively-Compact Spinor Vertices and Space-Time Spin-Locality in Higher-Spin Theory

The concepts of compact and projectively-compact spin-local spinor vertices are introduced. Vertices of this type are shown to be space-time spin-local, i.e. their restriction to any finite subset of fields is space-time local. The known spinor spin-local cubic vertices with the minimal number of space-time derivatives are verified to be projectively-compact. This has the important consequence that spinor spin-locality of the respective quartic vertices would imply their space-time spin-locality. More generally, it is argued that the proper class of solutions of the non-linear higher-spin equations that leads to the minimally non-local (presumably space-time spin-local) vertices is represented by the projectively-compact vertices. The related aspects of the higher-spin holographic correspondence are briefly discussed.

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arXiv2022

On the variational principle in the unfolded dynamics

The interplay between off-shell and on-shell unfolded systems is analysed. The formulation of invariant constraints that put an off-shell system on shell is developed by adding new variables and derivation in the target space, that extends the original $Q$-derivation of the unfolded system to a bicomplex. The analogue of the Euler-Lagrange equations in the unfolded dynamics is suggested. The general class of invariant on-shell equation constraints is defined in cohomological terms. The necessary and sufficient condition for the on-shell equation constraints being Euler-Lagrange for some Lagrangian system is proven. The proposed construction is illustrated by the scalar field example.

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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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