Maxim Grigoriev

Parent Field Theory and Unfolding in BRST First-Quantized Terms

For free-field theories associated with BRST first-quantized gauge systems, we identify generalized auxiliary fields and pure gauge variables already at the first-quantized level as the fields associated with algebraically contractible pairs for the BRST operator. Locality of the field theory is taken into account by separating the space–time degrees of freedom from the internal ones. A standard extension of the first-quantized system, originally developed to study quantization on curved manifolds, is used here for the construction of a first-order parent field theory that has a remarkable property: by elimination of generalized auxiliary fields, it can be reduced both to the field theory corresponding to the original system and to its unfolded formulation. As an application, we consider the free higher-spin gauge theories of Fronsdal.

Unified BRST description of AdS gauge fields

Abstract A concise formulation for mixed-symmetry gauge fields on AdS space is proposed. It is explicitly local, gauge invariant, and has manifest AdS symmetry. Various other known formulations (including the original formulation of Metsaev and the unfolded formulation) can be derived through the appropriate reductions and gauge fixing. As a byproduct, we also identify some new useful formulations of the theory that can be interesting for further developments. The formulation is presented in the BRST terms and extensively uses Howe duality. In particular, the BRST operator is a sum of the term associated to the spacetime isometry algebra and the term associated to the Howe dual symplectic algebra.

Higher-order singletons, partially massless fields, and their boundary values in the ambient approach

Abstract Using ambient space we develop a fully gauge and o ( d , 2 ) -covariant approach to boundary values of AdS d + 1 gauge fields. It is applied to the study of (partially) massless fields in the bulk and (higher-order) conformal scalars, i.e. singletons, as well as (higher-depth) conformal gauge fields on the boundary. In particular, we identify the corresponding generalized Fradkin–Tseytlin equations as obstructions to the extension of the off-shell boundary value to the bulk, generalizing the usual considerations for the holographic anomalies to the partially massless fields. We also relate the background fields for the higher-order singleton to the boundary values of partially massless fields and prove the appropriate generalization of the Flato–Fronsdal theorem, which is in agreement with the known structure of symmetries for the higher-order wave operator. All these facts support the following generalization of the higher-spin holographic duality: the O ( N ) model at a multicritical isotropic Lifshitz point should be dual to the theory of partially massless symmetric tensor fields described by the Vasiliev equations based on the higher-order singleton symmetry algebra.

Massless Poincare modules and gauge invariant equations

Abstract Starting with an indecomposable Poincare module M 0 induced from a given irreducible Lorentz module we construct a free Poincare invariant gauge theory defined on the Minkowski space. The space of its gauge inequivalent solutions coincides with (in general, is closely related to) the starting point module M 0 . We show that for a class of indecomposable Poincare modules the resulting theory is a Lagrangian gauge theory of the mixed-symmetry higher spin fields. The procedure is based on constructing the parent formulation of the theory. The Labastida formulation and the unfolded description of the mixed-symmetry fields are reproduced through the appropriate reductions of the parent formulation. As an independent check we show that in the momentum representation the solutions form a unitary irreducible Poincare module determined by the respective module of the Wigner little group.

Manifestly conformal descriptions and higher symmetries of bosonic singletons

The usual ambient space approach to conformal fields is based on identifying the d-dimensional conformal space as the Dirac projective hypercone in a flat d+2-dimensional ambient space. In this work, we explicitly concentrate on singletons of any integer spin and propose an approach that allows one to have both locality and conformal symmetry manifest. This is achieved by using the ambient space representation in the fiber rather than in spacetime. This approach allows us to characterize a subalgebra of higher symmetries for any bosonic singleton, which is a candidate higher-spin algebra for mixed symmetry gauge fields on anti de Sitter spacetime. Furthermore, we argue that this algebra actually exhausts all higher symmetries.

Parent form for higher spin fields on anti-de Sitter space

We construct a first order parent field theory for free higher spin gauge fields on constant curvature spaces. As in the previously considered flat case, both the original formulation by Fronsdal and the unfolded one by Vasiliev can be reached by two different straightforward reductions. The parent theory itself is formulated using a higher dimensional embedding space. It turns out to be geometrically extremely transparent and free of the intricacies of both of its reductions.

Unified BRST approach to (partially) massless and massive AdS fields of arbitrary symmetry type

Abstract We construct a concise gauge invariant formulation for massless, partially massless, and massive bosonic AdS fields of arbitrary symmetry type at the level of equations of motion. Our formulation admits two equivalent descriptions: in terms of the ambient space and in terms of an appropriate vector bundle, as an explicitly local first-order BRST formalism. The second version is a parent-like formulation that can be used to generate various other formulations via equivalent reductions. In particular, we demonstrate a relation to the unfolded description of massless and partially massless fields.

Seiberg-Witten maps and noncommutative Yang-Mills theories for arbitrary gauge groups

Seiberg-Witten maps and a recently proposed construction of noncommutative Yang-Mills theories (with matter fields) for arbitrary gauge groups are reformulated so that their existence to all orders is manifest. The ambiguities of the construction which originate from the freedom in the Seiberg-Witten map are discussed with regard to the question whether they can lead to inequivalent models, i.e., models not related by field redefinitions.

Notes on the ambient approach to boundary values of AdS gauge fields

The ambient space allows us to formulate both fields on AdSd + 1 and conformal fields in d dimensions such that the symmetry algebra is realized linearly. We elaborate an ambient approach to the boundary analysis of gauge fields on AdSd + 1 spacetime. More technically, we use its parent extension where fields are still defined on AdS or conformal space through arbitrary intrinsic coordinates while the ambient construction works in the target space. In this way, a manifestly local and -covariant formulation of the boundary behavior of massless symmetric tensor gauge fields on AdSd + 1 spacetime is obtained. As a byproduct, we identify some useful ambient formulation for Fronsdal fields, conformal currents and shadow fields along with a concise generating-function formulation of the Fradkin?Tseytlin conformal fields somewhat similar to the one obtained by Metsaev. We also show how this approach extends to more general gauge theories and discuss its relation to the unfolded derivation of the boundary dynamics recently proposed by Vasiliev.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ?Higher spin theories and holography?.

Massive higher spins from BRST and tractors

Abstract We obtain the higher spin tractor equations of motion conjectured by Gover et al. from a BRST approach and use those methods to prove that they describe massive, partially massless and massless higher spins in conformally flat backgrounds. The tractor description makes invariance under local choices of unit systems manifest. In this approach, physical models are described by conformal, rather than (pseudo-)Riemannian geometry. In particular masses become geometric quantities, namely the weights of tractor fields. Massive models can therefore be handled in a unified and simple manner mimicking the gauge principle usually employed for massless models. From a holographic viewpoint, these models describe both the bulk and boundary theories in terms of conformal geometry. This is an important advance, because tying the boundary conformal structure to that of the bulk theory gives greater control over a bulk–boundary correspondence.