Ruben Manvelyan

The group approach to AdS space propagators: a fast algorithm

In this paper we show how the method of [4] for the calculation of two-point functions in (d + 1)-dimensional AdS space can be simplified. This results in an algorithm for the evaluation of the two-point functions as linear combinations of Legendre functions of the second kind. This algorithm can be easily implemented on a computer. For the sake of illustration, we displayed the results for the case of symmetric traceless tensor fields with rank up to l = 4.

TRACE ANOMALIES AND COCYCLES OF WEYL AND DIFFEOMORPHISMS GROUPS

The general structure of trace anomaly, suggested recently by Deser and Schwimmer is argued to be the consequence of the Wess-Zumino consistency condition. The response of partition function on a finite Weyl transformation, which is connected with the cocycles of the Weyl group in d=2k dimensions is considered, and explicit answers for d=4, 6 are obtained. In particular, it is shown that addition of the special combination of the local counterterms leads to the simple form of that cocycle, quadratic over Weyl field σ, i.e. the form, similar to the two-dimensional Liouville action. This form also establishes the connection of the cocycles with conformal-invariant operators of order d and zero weight. We also give the general rule for transformation of that cocycles into the cocycles of diffeomorphisms group.

Trace anomalies and cocycles of the Weyl group

Abstract The response of the partition function of six-dimensional classically Weyl-invariant theories on a finite Weyl transformation is calculated (this is a cocycle of the Weyl group, connected with the trace anomaly), and it is shown that this cocycle can be chosen quadratic over the Weyl field, in exact analogy with the two-dimensional Liouville action: S = ∫ d 6 x g (σΔ 6 σ+σ × Anomaly ) where Δ 6 is the zero weight conformal-invariant operator of order six, derived in the present letter. The structure of the trace anomaly as a direct consequence of the Wess-Zumino consistensy condition is discussed.

Off-shell superconformal higher spin multiplets in four dimensions

A bstractWe formulate off-shell N

On higher spin symmetries in AdS 5

\mathcal{N}

Geometrical action for w∞ algebra as a reduced symplectic Chern-Simons theory

= 1 superconformal higher spin multiplets in four spacetime dimensions and briefly discuss their coupling to conformal supergravity. As an example, we explicitly work out the coupling of the superconformal gravitino multiplet to conformal supergravity. The corresponding action is super-Weyl invariant for arbitrary supergravity backgrounds. However, it is gauge invariant only if the supersymmetric Bach tensor vanishes. This is similar to linearised conformal supergravity in curved background.

Geometrical action for w±∞ algebras

Abstract The effective action for 2 d -gravity with manifest area-preserving invariance is obtained in the flat and in the general gravitational background. The cocyclic properties of the last action are proved, and generalizations on higher dimensions are discussed.

Super-Weyl cocycle in d = 4 and superconformal-invariant operator

A bstractA special embedding of the SU(4) algebra in SU(10), including both spin two and spin three symmetry generators, is constructed. A possible five dimensional action for massless spin two and three fields with cubic interaction is constructed. The connection with the previously investigated higher spin theories in AdS5 background is discussed. Generalization to the more general case of symmetries, including spins 2, 3, . . . s, is shown.