Superconformal and Super-BRS Invariance of the N = 1 Supersymmetric WZW Model Based on Lie Superalgebra

We study the superconformal and super-BRS invariance of the supersymmetric Wess-Zumino-Witten model based on Lie superalgebra. The computation of the critical super-dimension of this model is done using the Fujikawa regularization. Finally, we recover the well-known result which fixes the relative coupling constant a2 = 1 in a rigorous way.Comment: 14 page

Composite fields, generalized hypergeometric functions and the U(1)YU(1)_Y symmetry in the AdS/CFT correspondence

We discuss the concept of composite fields in flat CFT as well as in the context of AdS/CFT. Furthermore we show how to represent Green functions using generalized hypergeometric functions and apply these techniques to four-point functions. Finally we prove an identity of $U(1)_Y$ symmetry for four-point functions.Comment: 12 pages, 2 figure

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

Maps between Deformed and Ordinary Gauge Fields

In this paper, we introduce a map between the q-deformed gauge fields defined on the GL$_{q}(N)$-covariant quantum hyperplane and the ordinary gauge fields. Perturbative analysis of the q-deformed QED at the classical level is presented and gauge fixing $\grave{a}$ la BRST is discussed. An other star product defined on the hybrid $(q,h)$% -plane is explicitly constructed .Comment: 10 page

q-deformed conformal correlation functions

A q-analogue of four dimensional conformally invariant field theory based on the quantum algebra U_{q}(so(4,2)) is proposed. The two- and three-point correlation functions are calculated. The construction is elaborated in order to fit the Hopf algebra structure.Comment: 13 pages, minor corrections, Journal-ref adde

Conformal partial wave analysis of AdS amplitudes for dilaton-axion four-point functions

Operator product expansions are applied to dilaton-axion four-point functions. In the expansions of the bilocal fields $\tilde{\Phi}\tilde{\Phi}$, $\tilde{C}\tilde{C}$ and $\tilde{\Phi}\tilde{C}$, the conformal fields which are symmetric traceless tensors of rank $l$ and have dimensions $\delta=2+l$ or $8+l+\eta(l)$ and $\eta(l)=\mathcal{O}(N^{-2})$ are identified. The unidentified fields have dimension $\delta=\lambda+l+\eta(l)$ with $\lambda\geq 10$. The anomalous dimensions $\eta(l)$ are calculated at order $\mathcal{O}(N^{-2})$ for both $2^{-{1/2}}(-\tilde{\Phi}\tilde{\Phi} + \tilde{C}\tilde{C})$ and $2^{-{1/2}}(\tilde{\Phi}\tilde{C} + \tilde{C}\tilde{\Phi})$ and are found to be the same, proving $U(1)_Y$ symmetry. The relevant coupling constants are given at order $\mathcal{O}(1)$.Comment: 27 pages, 1 graph, 12 figures, Corrections in eqns. (1.10), (1.11