arXiv subjects

K. A. Ushakov

Publications and source records attributed to K. A. Ushakov.

4 recordsLinked to original sources

arXiv2026

The $σ_-$ Cohomology Analysis for Coxeter HS $B_2$ model

The dynamical content of equations resulting from rank-two covariant derivatives in $B_2$ Coxeter theory in $AdS_4$ are analyzed in terms of $σ_-$-complexes. Primary fields and gauge-invariant differential operators on primary fields are classified for $(adj \otimes adj)$ one-form fields $ω$ and $(tw\otimes adj)$ zero-form fields $C$. It is shown that one-forms $ω$ in the $(adj \otimes adj)$ sector encode symmetric massless fields and partially massless fields of all spins and depth of masslessness. Gluing of the one-form module to the zero-form modules at the linear vertices is studied.

hep-th↗

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.

hep-th↗

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.

hep-th↗

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.

hep-th↗