Mikhail A. Vasiliev

Nonlinear equations for symmetric massless higher spin fields in (A)dSd

Nonlinear field equations for totally symmetric bosonic massless fields of all spins in any dimension are presented.Nonlinear field equations for totally symmetric bosonic massless fields of all spins in any dimension are presented.

Consistent equations for interacting gauge fields of all spins in 3+1 dimensions

Abstract Consistent equations of motion of interacting gauge fields of all spins in 3+1 dimensions are formulated in a closed form. These equations are explicitly general coordinate invariant, possess all necessary higher spin gauge symmetries and reduce to the usual equations of free massless fields of all spin s=0, 1 2 , 1, …, ∞ at the linearized level. In the spin-2 sector, the proposed equations are equivalent to the Einstein equations with the cosmological term.

Higher spin gauge theories: Star product and AdS space

We review the theory of higher spin gauge fields in 2+1 and 3+1 dimensional anti-de Sitter space and present some new results on the structure of higher spin currents and explicit solutions of the massless equations. A previously obtained d=3 integrating flow is generalized to d=4 and is shown to give rise to a perturbative solution of the d=4 nonlinear higher spin equations. A particular attention is paid to the relationship between the star-product origin of the higher spin symmetries, AdS geometry and the concept of space-time locality.

On the gravitational interaction of massless higher-spin fields

Abstract We show that, despite a widespread belief, the gravitational interaction of massless higher-spin fields (s > 2) does exist at least in the first nontrivial order. The principal novel feature of the gravitational higher-spin interaction is its non-analyticity in the cosmological constant. Our construction is based on an infinite-dimensional higher-spin superalgebra proposed previously that leads to an infinite system of all spins s > 1.

Cubic Interaction in Extended Theories of Massless Higher Spin Fields

Abstract A cubic interaction of all massless higher-spin fields with s ⩾ 1 is constructed, based on the extended higher-spin superalgebras suggested previously by one of us (M.V.). This interaction incorporates gravitational and Yang-Mills interactions of massless higher-spin fields, which turn out to be consistent in the cubic order. An essential novel feature of the gravitational higher-spin interaction is its non-analyticity in the cosmological constant. An explicit form is found for deformed higher-spin gauge transformations leaving the action invariant.

More on equations of motion for interacting massless fields of all spins in 3+1 dimensions

Abstract We establish the simple link between the recently proposed equations of motion for interacting massless fields of all spins 0⩽ s

Higher-spin gauge interactions for massive matter fields in 3D AdS space-time

A remarkable feature of the models with interactions exhibiting higher-spin (HS) gauge symmetries in d > 2 is that their most symmetric vacua require the (anti)-de Sitter (AdS) geometry rather than the flat geometry. In striking parallelism to what might be expected of M-theory, HS gauge theories describe infinite towers of fields of all spins and possess naturally space-time SUSY and Chan-Paton type inner symmetries. In this paper, we analyze at the level of the equations of motion the simplest non-trivial HS model which describes HS gauge interactions (on the top of the usual supergravitational and (Chern-Simons) Yang-Mills interactions) of massive spin-0 and spin-12 matter fields in d = 2 + 1 AdS space-time. The parameter of mass of the matter fields is identified with the vev of a certain auxiliary field in the model. The matter fields are shown to be arranged into 3d N = 2 massive hypermultiplets in certain representations of U(n) × U(m) Yang-Mills gauge groups. Discrete symmetries of the full system are studied, and the related N = 1 supersymmetric truncations with O(n) and Sp(n) Yang-Mills symmetries are constructed. The simplicity of the model allows us to elucidate some general properties of the HS models. In particular, a new result, which can have interesting implications to the higher-dimensional models, is that our model is shown to admit an “integrating” flow that proves existence of a non-local Backlund-Nicolai-type mapping to the free system.

Consistent equations for interacting massless fields of all spins in the first order in curvatures

Abstract A new form of equations of motion is suggested for d =4 massless fields of all spins interacting with gravity: equations of all massless fields, including the gravitational field itself, are described in terms of a free differential algebra constructed from 1-forms and 0-forms belonging both to the adjoint representation of the superalgebra of higher-spin and auxiliary fields proposed previously by E. S. Fradkin and the author. In this construction, 1-forms describe gauge massless and auxiliary fields, while 0-forms describe lower-spin fields and Weyl tensors corresponding to gauge 1-forms. The equations of motion are constructed explicitly in the first order in the Weyl 0-forms (and in all orders in 1-forms) that exceeds significantly the results of E. S. Fradkin and M. A. Vasiliev ( Phys. Lett. B 189 (1987), 89; Nucl. Phys. B 291 (1987), 141) on the cubic higher-spin-gravitational interaction. The equations obtained are shown to remain consistent when all quantities take on their values in an arbitrary associative algebra. This enables us to describe simultaneously a class of extended-type theories with Yang-Mills gauge groups U ( n ) × U ( n ) corresponding to massless spin-1 fields ( n is arbitrary). Various consistent truncations of these extended theories are also dicussed including those with Yang-Mills gauge groups SO ( n ) × SO ( n ).

HIGHER-SPIN GAUGE THEORIES IN FOUR, THREE AND TWO DIMENSIONS

We review the theory of higher-spin gauge fields in four and three space-time dimensions and present some new results on higher-spin gauge interactions of matter fields in two dimensions.

Candidate for the role of higher-spin symmetry

Infinite-dimensional non-abelian superalgebras, related to interacting massless higher-spin fields of all spins s ⩾ 3/2, are proposed. Conditions are formulated that provide uniqueness for these higher-spin superalgebras, denoted as shsρ(1) (ρ = 0 or 1). Among these conditions, the major role is played by the requirement that linearized curvatures of shsρ(1) coincide with the linearized higher-spin curvatures obtained previously. Subalgebras and contractions of shsρ(1) are considered. A higher-spin interaction, which is introduced in terms of the shsρ(1) curvatures, is discussed briefly. It is found that a gravitational interaction of massless higher spins requires non-analyticity in the cosmological constant.