arXiv subjects

M. A. Vasiliev

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

At least 37 records · Page 2Linked to original sources

arXiv2020

Nonlinear higher spin theories in various dimensions

In this article, an introduction to the nonlinear equations for completely symmetric bosonic higher spin gauge fields in anti de Sitter space of any dimension is provided. To make the presentation self-contained we explain in detail some related issues such as the MacDowell-Mansouri-Stelle-West formulation of gravity, unfolded formulation of dynamical systems in terms of free differential algebras and Young tableaux symmetry properties in terms of Howe dual algebras.

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arXiv2020

Spin-Locality of Higher-Spin Theories and Star-Product Functional Classes

The analysis of spin-locality of higher-spin gauge theory is formulated in terms of star-product functional classes appropriate for the $β\to -\infty$ limiting shifted homotopy proposed recently in arXiv:1909.04876 where all $ω^2 C^2$ higher-spin vertices were shown to be spin-local. For the $β\to -\infty$ limiting shifted contracting homotopy we identify the class of functions ${\mathcal H}^{+0}$, that do not contribute to the r.h.s. of HS field equations at a given order. A number of theorems and relations that organize analysis of the higher-spin equations are derived including extension of the Pfaffian Locality Theorem of arXiv:1805.11941 to the $β$-shifted contracting homotopy and the relation underlying locality of the $ω^2 C^2$ sector of higher-spin equations. Space-time interpretation of spin-locality of theories involving infinite towers of fields is proposed as the property that the theory is space-time local in terms of original constituent fields $Φ$ and their local currents $J(Φ)$ of all ranks. Spin-locality is argued to be a proper substitute of locality for theories with finite sets of fields for which the two concepts are equivalent.

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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

Field Equations for the Simplest Multi-Particle Higher-Spin Systems

We derive the product law for the simplest multi-particle higher-spin algebra $M_2(A)$ and its factor-algebra $M^2(A)$ with rank-one fields factored out. Equations of motion for the systems resulting from these algebras are analysed. We conclude that the equations for $M_2(A)$ describe the conformal off-shell higher-spin system with the rank-two fields representing the off-shell degrees of freedom of the originally massless system. On the other hand the equations resulting from $M^2(A)$ describe the infinite system of conserved currents unrelated to massless fields.

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arXiv2018

Scattering amplitudes as multi-particle higher-spin charges in the correspondence space

Following the proposal of arXiv:1312.6673, multi-particle scattering amplitudes are represented as conserved higher-spin charges. The advantage of such reformulation is that multi-particle amplitudes acquire the form of an integral of a closed form in the correspondence unifying usual space-time with the twistor-like spinor space. This allows one to identify seemingly different formulae for amplitudes in terms of twistor and space-time integrals. Example of tree MHV amplitudes of Yang-Mills theory is considered in detail. Our results are derived using unfolded dynamics formulation of massless fields. In these terms all information on the amplitude is contained in a single function $η$ that, even for lower spin amplitudes, can be interpreted as a higher-spin symmetry parameter. The proposed technique can be useful to relate different approaches to amplitude calculations.

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arXiv2018

Homotopy Operators and Locality Theorems in Higher-Spin Equations

A new class of shifted homotopy operators in higher-spin gauge theory is introduced. A sufficient condition for locality of dynamical equations is formulated and Pfaffian Locality Theorem identifying a subclass of shifted homotopies that decrease the degree of non-locality in higher orders of the perturbative expansion is proven.

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arXiv2018

From Coxeter Higher-Spin Theories to Strings and Tensor Models

A new class of higher-spin gauge theories associated with various Coxeter groups is proposed. The emphasize is on the $B_p$--models. The cases of $B_1$ and its infinite graded-symmetric product $sym\,(\times B_1)^\infty$ correspond to the usual higher-spin theory and its multi-particle extension, respectively. The multi-particle $B_2$--higher-spin theory is conjectured to be associated with String Theory. $B_p$--higher-spin models with $p>2$ are anticipated to be dual to the rank-$p$ boundary tensor sigma-models. $B_p$ higher-spin models with $p\geq 2$ possess two coupling constants responsible for higher-spin interactions in $AdS$ background and stringy/tensor effects, respectively. The brane-like idempotent extension of the Coxeter higher-spin theory is proposed allowing to unify in the same model the fields supported by space-times of different dimensions. Consistency of the holographic interpretation of the boundary matrix-like model in the $B_2$-higher-spin model is shown to demand $N\geq 4$ SUSY, suggesting duality with the $N=4$ SYM upon spontaneous breaking of higher-spin symmetries. The proposed models are shown to admit unitary truncations.

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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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arXiv2018

Current Interactions from the One-Form Sector of Nonlinear Higher-Spin Equations

The form of higher-spin current interactions in the sector of one-forms is derived from the nonlinear higher-spin equations in $AdS_4$. Quadratic corrections to higher-spin equations are shown to be independent of the phase of the parameter $η=\exp iφ$ in the full nonlinear higher-spin equations. The current deformation resulting from the nonlinear higher-spin equations is represented in the canonical form with the minimal number of space-time derivatives. The non-zero spin-dependent coupling constants of the resulting currents are determined in terms of the higher-spin coupling constant $η\barη$. Our results confirm the conjecture that (anti-)self-dual nonlinear higher-spin equations result from the full system at ($η=0$) $\bar η=0$.

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arXiv2018

On the Local Frame in Nonlinear Higher-Spin Equations

Properties of the resolution operator ${\rm d}_{loc}^*$ in higher-spin equations, that leads to local current interactions at the cubic order and minimally nonlocal higher-order corrections, are formulated in terms of the condition on the class of master fields of higher-spin theory that restricts both the dependence on the spinor $Y$, $Z$ variables and on the contractions of indices between the constituent fields in bilinear terms. The Green function in the sector of zero-forms is found for the case of constituent fields carrying helicities of opposite signs. It is shown that the local resolution ${\rm d}_{loc}^*$ differs from the conventional De Rham resolution ${\rm d}_Z^*$ by a non-local shift.

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arXiv2017

Current Interactions and Holography from the 0-Form Sector of Nonlinear Higher-Spin Equations

The form of higher-spin current interactions in $AdS_4$ is derived from the full nonlinear higher-spin equations in the sector of Weyl 0-forms. The coupling constant in front of spin-one currents built from scalars and spinors as well as Yukawa coupling are determined explicitly. Couplings of all other higher-spin current interactions are determined implicitly. All couplings are shown to be independent of the phase parameter of the nonlinear higher-spin theory. The proper holographic dependence of the vertex on the higher-spin phase parameter is shown to result from the boundary conditions on the bulk fields.

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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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arXiv2017

Charges in nonlinear higher-spin theory

Nonlinear higher-spin equations in four dimensions admit a closed two-form that defines a gauge-invariant global charge as an integral over a two-dimensional cycle. In this paper we argue that this charge gives rise to partitions depending on various lower- and higher-spin chemical potentials identified with modules of topological fields in the theory. The vacuum contribution to the partition is calculated to the first nontrivial order for a solution to higher-spin equations that generalizes AdS4 Kerr black hole of General Relativity. The resulting partition is non-zero being in parametric agreement with the ADM-like behavior of a rotating source. The linear response of chemical potentials to the partition function is also extracted. The explicit unfolded form of 4d GR black holes is given. An explicit formula relating asymptotic higher-spin charges expressed in terms of the generalized higher-spin Weyl tensor with those expressed in terms of Fronsdal fields is obtained.

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arXiv2017

Invariant Functionals in Higher-Spin Theory

A new construction for gauge invariant functionals in the nonlinear higher-spin theory is proposed. Being supported by differential forms closed by virtue of the higher-spin equations, invariant functionals are associated with central elements of the higher-spin algebra. In the on-shell $AdS_4$ higher-spin theory we identify a four-form conjectured to represent the generating functional for $3d$ boundary correlators and a two-form argued to support charges for black hole solutions. Two actions for $3d$ boundary conformal higher-spin theory are associated with the two parity-invariant higher-spin models in $AdS_4$. The peculiarity of the spinorial formulation of the on-shell $AdS_3$ higher-spin theory, where the invariant functional is supported by a two-form, is conjectured to be related to the holomorphic factorization at the boundary. The nonlinear part of the star-product function $F_*(B(x))$ in the higher-spin equations is argued to lead to divergencies in the boundary limit representing singularities at coinciding boundary space-time points of the factors of $B(x)$, which can be regularized by the point splitting. An interpretation of the RG flow in terms of proposed construction is briefly discussed.

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arXiv2016

Higher-spin fields and charges in the periodic spinor space

The $sp(2M)$ invariant unfolded system is considered in the periodic twistor-like spinor space. Complete set of non-trivial charges corresponding to the global symmetry compatible with the periodicity conditions is constructed. Residual infinite-dimensional symmetry is realized in terms of the star-product algebra. It is shown that charges associated with integrations over different cycles are related by particular higher-spin symmetry transformations.

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arXiv2016

Higher-Rank Fields and Currents

$Sp(2M)$ invariant field equations in the space ${\cal M}_M$ with symmetric matrix coordinates are classified. Analogous results are obtained for Minkowski-like subspaces of ${\cal M}_M$ which include usual $4d$ Minkowski space as a particular case. The constructed equations are associated with the tensor products of the Fock (singleton) representation of $Sp(2M)$ of any rank ${\mathbf{r }}$. The infinite set of higher-spin conserved currents multilinear in rank-one fields in ${\cal M}_M$ is found. The associated conserved charges are supported by $({\mathbf{r }} M-\frac{\mathbf{r } ({\mathbf{r }} -1)}{2})-$dimensional differential forms in ${\cal M}_M$, that are closed by virtue of the rank-$2{\mathbf{r }}$ field equations. The cohomology groups $H^p(σ^{\mathbf{r }}_-)$ with all $p$ and ${\mathbf{r }}$, which determine the form of appropriate gauge fields and their field equations, are found both for ${\cal M}_M$ and for its Minkowski-like subspace.

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arXiv2016

Perturbative analysis in higher-spin theories

A new scheme of the perturbative analysis of the nonlinear HS equations is developed giving directly the final result for the successive application of the homotopy integrations which appear in the standard approach. It drastically simplifies the analysis and results from the application of the standard spectral sequence approach to the higher-spin covariant derivatives, allowing us in particular to reduce multiple homotopy integrals resulting from the successive application of the homotopy trick to a single integral. Efficiency of the proposed method is illustrated by various examples. In particular, it is shown how the Central on-shell theorem of the free theory immediately results from the nonlinear HS field equations with no intermediate computations.

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arXiv2016

Symmetries of higher-spin current interactions in four dimensions

Current interaction of massless fields in four dimensions is shown to break sp (8) symmetry of free massless equations of all spins down to the conformal symmetry su (2,2). This breaking is in agreement with the form of nonlinear higher-spin field equations.

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