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By using the approach of non-commutative geometry, we study spinors and scalars on the two layers AdS$_{d+1}$ space. We have found that in the boundary of two layers AdS$_{d+1}$ space, by using the AdS/CFT correspondence, we have a logarithmic conformal field theory. This observation propose a way to get the quantum field theory in the context of non-commutative geometry., Comment: some minor typographical errors are corrected, to appear in Phys. Lett. B

We generalize the Maldacena correspondence to the logarithmic conformal field theories. We study the correspondence between field theories in (d+1)-dimensional AdS space and the d-dimensional logarithmic conformal field theories in the boundary of $AdS_{d+1}$. Using this correspondence, we get the n-point functions of the corresponding logarithmic conformal field theory in d-dimensions., Comment: 10 pages, LaTeX. A paragraph was added. To appear in Int. J. Mod. Phys. A

By taking the interacting spinor-scalar theory on the $AdS_{d+1}$ space we calculate the boundary CFT correlation functions using AdS/CFT correspondence., Comment: The crucial role of the surface term in the action to generate the correlation functions quadratic in spinors is considered. LaTeX file, 8 pages

We obtain the periods and one-instanton coefficient of the N=2 superrsymmetric Yang-Mills theory with the exceptional gauge group E_6. These calculations are based on the E_6 spectral curve and the obtained one-instanton coefficient is in agreement with the microscopic results., Comment: 11 pages, LaTex, no figures

We obtain the Picard-Fuchs equations of N=2 supersymmetric Yang-Mills theory with the exceptional gauge group E_6. Such equations are based on E_6 spectral curve., Comment: Latex, 5 pages, few misprints are corrected, conclusion is added

We define transformation of multiplets of fields (Jordan cells) under the D-dimensional conformal group, and calculate two and three point functions of fields, which show logarithmic behaviour. We also show how by a formal differentiation procedure, one can obtain n-point function of logarithmic field theory from those of ordinary conformal field theory., Comment: 9 pages, LaTeX, some misprints are corrected, to be published in Phys. Lett. B

We consider the standard vector and chiral gauged WZNW models by their gauged maximal null subgroups and show that they can be mapped to each other by a special transformation. We give an explicit expression for the map in the case of the classical Lie groups $ A_N $, $ B_N $, $ C_N $, $ D_N $, and note its connection with the duality map for the Riemmanian globally symmetric spaces., Comment: 13 pages, LaTeX