Konstantin Alkalaev

On the frame-like formulation of mixed-symmetry massless fields in (A)dSd

Abstract The frame-like covariant Lagrangian formulation of bosonic and fermionic mixed-symmetry type higher spin massless fields propagating on the AdS d background is proposed. Higher spin fields are described in terms of gauge p -forms which carry tangent indices representing certain traceless tensor or gamma transversal spinor-tensor representations of the AdS d algebra o ( d −1,2) (or o ( d ,1) for bosonic fields in dS d ). Manifestly gauge invariant Abelian higher spin field strengths are introduced for the general case. We describe the general framework and demonstrate how it works for the mixed-symmetry type fields associated with the three-cell “hook” and arbitrary two-row rectangular tableaux. The manifestly gauge invariant actions for these fields are presented in a simple form. The flat limit is also analyzed.

N=1 supersymmetric theory of higher spin gauge fields in AdS5 at the cubic level

Abstract We formulate gauge invariant interactions of totally symmetric tensor and tensor-spinor higher spin gauge fields in AdS 5 that properly account for higher-spin-gravitational interactions at the action level in the first non-trivial order.

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.

Lagrangian formulation for free mixed-symmetry bosonic gauge fields in (A)dSd

Covariant lagrangian formulation for free bosonic massless fields of arbitrary mixed-symmetry type in (A)dSd space-time is presented. The analysis is based on the frame-like formulation of higher-spin field dynamics [1] with higher-spin fields described as p-forms taking values in appropriate modules of the (A)dSd algebra. The problem of finding free field action is reduced to the analysis of an appropriate differential complex, with the derivation associated with the variation of the action. The constructed action exhibits additional gauge symmetries in the flat limit in agreement with the general structure of gauge symmetries for mixed-symmetry fields in Minkowski and (A)dSd spaces.

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.

FV-type action for AdS 5 mixed-symmetry fields

We formulate Fradkin-Vasiliev type theory of massless higher spin fields in AdS5. The corresponding action functional describes cubic order approximation to gravitational interactions of bosonic mixed-symmetry fields of a particular “hook” symmetry type and totally symmetric bosonic and fermionic fields.

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.

Massless hook field in AdS d +1 from the holographic perspective

A bstractWe systematically consider the AdS/CFT correspondence for a simplest mixed- symmetry massless gauge field described by hook Young diagram. We introduce the radial gauge fixing and explicitly solve the Dirichlet problem for the hook field equations. Solution finding conveniently splits in two steps. We first define an incomplete solution characterized by a functional freedom and then impose the boundary conditions. The resulting complete solution is fixed unambiguously up to boundary values. Two-point correlation function of hook primary operators is found via the corresponding boundary effective action computed separately in even and odd boundary dimensions. In particular, the higher-derivative action for boundary conformal hook fields is identified with a singular part of the effective action in even dimensions. The bulk/boundary symmetry transmutation within the Dirichlet boundary problem is explicitly studied. It is shown that traces of boundary fields are Stueckelberg-like modes that can be algebraically gauged away so that boundary fields are traceless.

Conformal blocks of WN minimal models and AGT correspondence

A bstractWe study the AGT correspondence between four-dimensional supersymmetric gauge field theory and two-dimensional conformal field theories in the context of WN