arXiv subjects
Publications and source records attributed to M. A. Vasiliev.
General aspects of higher-spin gauge theory and unfolded formulation are briefly recalled with some emphasize on the recent results on the breaking of $sp(8)$ symmetry by current interactions and construction of invariant functionals relevant to the higher-spin holography.
Gauge invariant conserved conformal currents built from massless fields of all spins in 4d Minkowski space-time and $AdS_4$ are described within the unfolded dynamics approach. The current cohomology associated with non-zero conserved charges is found. The resulting list of charges is shown to match the space of parameters of the conformal higher-spin symmetry algebra in four dimensions.
Properties of the functional classes of star-product elements associated with higher-spin gauge fields and gauge parameters are elaborated. Cohomological interpretation of the nonlinear higher-spin equations is given. An algebra ${\mathcal H}$, where solutions of the nonlinear higher-spin equations are valued, is found. A conjecture on the classes of star-product functions underlying (non)local maps and gauge transformations in the nonlinear higher-spin theory is proposed.
Interactions of massless fields of all spins in four dimensions with currents of any spin is shown to result from a solution of the linear problem that describes a gluing between rank-one (massless) system and rank-two (current) system in the unfolded dynamics approach. Since the rank-two system is dual to a free rank-one higher-dimensional system, that effectively describes conformal fields in six space-time dimensions, the constructed system can be interpreted as describing a mixture between linear conformal fields in four and six dimensions. Interpretation of the obtained results in spirit of AdS/CFT correspondence is discussed.
Conserved currents of any spin $t>0$ built from symmetric massless gauge fields of any integer spin $s \geq t$ in {4d} Minkowski space are found. In particular, stress-energy tensor for a higher-spin field of any spin is constructed. Analogously to spin-two stress (pseudo)tensor, currents considered in this paper are not gauge invariant. However, they are shown to generate gauge invariant conserved charges. Besides expected parity even HS currents, we found unexpected parity odd currents that generate less symmetries than the even ones. It is argued that these odd currents unlikely admit a consistent $AdS$ deformation.
We show how manifestly supersymmetric action for Wess-Zumino model can be constructed within the unfolded dynamics approach. The off-shell unfolded system for N = 1, D = 4 scalar supermultiplet is found. The action is presented in the form of integral of a closed 4-form over any (4, 0) surface in superspace as well as a superspace integral of an integral form or a chiral integral form. The proposed method is argued to provide a most general tool for the analysis of manifestly supersymmetric functionals.
Introductory lectures on higher-spin gauge theory given at 7 Aegean workshop on non-Einstein theories of gravity. The emphasis is on qualitative features of the higher-spin gauge theory and peculiarities of its space-time interpretation. In particular, it is explained that Riemannian geometry cannot play a fundamental role in the higher-spin gauge theory. The higher-spin symmetries are argued to occur at ultra high energy scales beyond the Planck scale. This suggests that the higher-spin gauge theory can help to understand Quantum Gravity. Various types of higher-spin dualities are briefly discussed.
We find exact spherically symmetric solution of 4d nonlinear bosonic higher-spin gauge theory, that preserves a quarter of supersymmetries of N=2 supersymmetric 4d higher-spin gauge theory. In the weak field regime it describes $AdS_4$ Schwarzschild black hole in the spin two sector along with non-zero massless fields of all integer spins.
Operator algebra of (not necessarily free) higher-spin conformal conserved currents in generalized matrix spaces, that include 3d Minkowski space-time as a particular case, is shown to be determined by an associative algebra $M$ of functions on the twistor space. For free conserved currents, $M$ is the universal enveloping algebra of the higher-spin algebra. Proposed construction greatly simplifies computation and analysis of correlators of conserved currents. Generating function for $n$-point functions of 3d (super)currents of all spins, built from $N$ free constituent massless scalars and spinors, is obtained in a concise form of certain determinant. Our results agree with and extend earlier bulk computations in the HS $AdS_4/CFT_3$ framework. Generating function for $n$-point functions of 4d conformal currents is also presented.
Multiparticle extension of a higher-spin algebra $l$ is introduced as the Lie superalgebra associated with the universal enveloping algebra $U(l)$. While conventional higher-spin symmetry does not mix $n$-particle states with different $n$, multiparticle symmetries do so. Quotients of multiparticle algebras are considered, that act on the space of $n$-particle states with $0\leq n\leq k$ analogous to the space of first $k$ Regge trajectories of String Theory. Original higher-spin algebra is reproduced at $k=1$. Full multiparticle algebras are conjectured to describe vacuum symmetries of string-like extensions of higher-spin gauge theories. Relation of the multiparticle algebras with 3d current operator algebras is described. The central charge parameter, to be related to the parameter ${\mathcal N}$ in $AdS/CFT$ correspondence, enters via the definition of supertrace. Extension to higher $p$-brane-like symmetries is introduced inductively.
Unfolded equations of motion for N = 1, D = 4 scalar supermultiplet are presented. We show how the superspace formulation emerges from the unfolded formulation. To analyze supersymmetric unfolded equations we extend the σ_-cohomology technics to the case with several operators σ_. The role of higher σ_-cohomology in the derivation of constraints is emphasized and illustrated by the example of scalar supermultiplet.
In this paper we discuss in detail the frame-like formulation of free bosonic massless higher-spin fields of general symmetry type in AdS(d), announced recently in hep-th/0311164, hep-th/0501108. Properties of gauge invariant and AdS covariant action functionals and their flat limits are carefully analyzed.
A new high-efficiency and low-background system for the measurement of natural gamma radioactivity in marine sediment and rock cores retrieved from beneath the seabed was designed, built, and installed on the JOIDES Resolution research vessel. The system includes eight large NaI(Tl) detectors that measure adjacent intervals of the core simultaneously, maximizing counting times and minimizing statistical error for the limited measurement times available during drilling expeditions. Effect to background ratio is maximized with passive lead shielding, including both ordinary and low-activity lead. Large-area plastic scintillator active shielding filters background associated with the high-energy part of cosmic radiation. The new system has at least an order of magnitude higher statistical reliability and significantly enhances data quality compared to other offshore natural gamma radiation (NGR) systems designed to measure geological core samples. Reliable correlations and interpretations of cored intervals are possible at rates of a few counts per second.
Unfolded equations of motion for symmetric massive bosonic fields of any spin in Minkowski and (A)dS spaces are presented. Manifestly gauge invariant action for a spin $s \ge 2$ massive field in any dimension is constructed in terms of gauge invariant curvatures.
The correspondence between BRST and unfolded formulations of field equations on group manifolds and homogeneous spaces is described. The previously introduced nonstandard BRST operator, that underlies Sp(2M) invariant higher-spin field equations, is shown to admit a natural oscillator-like realization. The coordinate independent form of conserved currents in the Sp(2M) invariant higher-spin theory is derived from the BRST formulation on Sp(2M) extended by the Heisenberg group.
We discuss twistor-like interpretation of the $Sp(8)$ invariant formulation of 4d massless fields in ten dimensional Lagrangian Grassmannian $Sp(8)/P$ which is the generalized space-time in this framework. The correspondence space $\mathbf{C}$ is $SpH(8)/PH$ where $SpH(8)$ is the semidirect product of $Sp(8)$ with Heisenberg group $\HG$ and $PH$ is some quasiparabolic subgroup of $SpH(8)$. Spaces of functions on $Sp(8)/P$ and $SpH(8)/PH$ consist of $Q_P $ closed functions on $Sp(8)$ and $Q_{PH} $ closed functions on $SpH(8)$, where $Q_P $ and $Q_{PH}$ are canonical BRST operators of $P$ and $PH$. The space of functions on the generalized twistor space $\mathbf{T}$ identifies with the $SpH(8)$ Fock module. Although $\mathbf{T}$ cannot be realized as a homogeneous space, we find a nonstandard $SpH(8)$ invariant BRST operator $\QQ$ $(\QQ^2 =0)$ that gives rise to an appropriate class of functions via the condition $\QQ f=0$ equivalent to the unfolded higher--spin equations. The proposed construction is manifestly $Sp(8)$ invariant, globally defined and coordinate independent. Its Minkowski analogue gives a version of twistor theory with both types of chiral spinors treated on equal footing. The extensions to the higher rank case with several Heisenberg groups and to the complex case are considered. A relation with Riemann theta functions, that are $\QQ$-closed, is discussed.
Free Lagrangians are found both for gauge and non-gauge bosonic conformal fields of any symmetry type and in any space-time dimension. Conformal gauge fields of various types, their gauge transformations and gauge invariant field strengths (generalized Weyl tensors), which are derived by the $σ_-$ cohomology technics in the frame-like formulation, are shown to correspond to supersymmetric vacua of certain supersymmetric matrix mechanics. The correspondence between conformal and $AdS_d$ higher-spin models, that turn out to have identical generalized Weyl tensors, is discussed.
Dynamics of four-dimensional massless fields of all spins is formulated in the Siegel space of complex $4\times 4$ symmetric matrices. It is shown that the unfolded equations of free massless fields, that have a form of multidimensional Schrodinger equations, naturally distinguish between positive- and negative-frequency solutions of relativistic field equations, i.e. particles and antiparticles. Multidimensional Riemann theta functions are shown to solve massless field equations in the Siegel space. We establish the correspondence between conserved higher-spin currents in four-dimensional Minkowski space and those in the ten-dimensional matrix space. It is shown that global symmetry parameters of the current in the matrix space should be singular to reproduce a nonzero current in Minkowski space. The $\D$-function integral evolution formulae for 4d massless fields in the Fock-Siegel space are obtained. The generalization of the proposed scheme to higher dimensions and systems of higher ranks is considered.