arXiv subjects

A. A. Tarusov

Publications and source records attributed to A. A. Tarusov.

5 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↗

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↗

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

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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