Exact solvability of the Calogero and Sutherland models

Translationally invariant symmetric polynomials as coordinates for n-body problems with identical particles are proposed. It is shown that in those coordinates the Calogero and Sutherland n-body Hamiltonians after appropriate gauge transformations can be presented as a {\it quadratic} polynomial in the generators of the algebra sl_n in finite-dimensional degenerate representations. The exact solvability of these models follows from the existence of the infinite flags of such representation spaces preserved by above Hamiltonians

The quantum one loop trace anomaly of the higher spin conformal conserved currents in the bulk of AdS4AdS_{4}

An analysis of the structure and singularities of the one loop two point function of the higher spin traceless and conserved currents constructed from the single scalar field in $AdS$ space is presented. The detailed renormalization procedure is constructed and the quantum violation of the traceless Ward identity is investigated. The connection with the one loop effective action for higher spin gauge fields is discussed.Comment: 23 pages, Latex, misprints corrected, v.3 two sections added, v.4 published version in Nucl. Phys.

AdS Box Graphs, Unitarity and Operator Product Expansions

We develop a method of singularity analysis for conformal graphs which, in particular, is applicable to the holographic image of AdS supergravity theory. It can be used to determine the critical exponents for any such graph in a given channel. These exponents determine the towers of conformal blocks that are exchanged in this channel. We analyze the scalar AdS box graph and show that it has the same critical exponents as the corresponding CFT box graph. Thus pairs of external fields couple to the same exchanged conformal blocks in both theories. This is looked upon as a general structural argument supporting the Maldacena hypothesis

The structure of the trace anomaly of higher spin conformal currents in the bulk of AdS4AdS_{4}

The two-point function of the conserved traceless spin-$\ell$ currents which are constructed from the scalar field $\sigma(z)$ is evaluated and renormalized by a dimensional regularization procedure. The anomaly is managed to arise only in the trace part. To isolate this trace anomaly it is sufficient to analyze only the maximum singular part of the two-point function and its trace terms to leading order. The corresponding part of the effective action which is quadratic in the trace of the higher spin field is explicitly given. For the spin-2 field which is identical with the gravitational field the results known from the literature are reproduced.Comment: latex, 21 pages,v.2 minor addition, ref. added, v.3 accepted in Nucl.Phys.

The group approach to AdS space propagators: A fast algorithm

In this letter 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.Comment: 14 pages, comment adde

The group approach to AdS space propagators

We show that AdS two-point functions can be obtained by connecting two points in the interior of AdS space with one point on its boundary by a dual pair of Dobrev's boundary-to-bulk intertwiners and integrating over the boundary point.Comment: 23 page