Quantizing field theories in noncommutative geometry and the correspondence between anti de Sitter space and conformal field theory

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.

Cosmological Solutions on Atiyah-Hitchin Space in Five Dimensional Einstein-Maxwell-Chern-Simons Theory

We construct non-stationary exact solutions to five dimensional Einstein-Maxwell-Chern-Simons theory with positive cosmological constant. The solutions are based on four-dimensional Atiyah-Hitchin space. In asymptotic regions, the solutions approach to Gibbons-Perry-Sorkin monopole solutions. On the other hand, near the four-dimensional bolt of Atiyah-Hitchin space, our solutions show a bolt structure in five dimensions. The c-function for the solutions shows monotonic increase in time, in agreement with the general expected behaviour of c-function in asymptotically dS spacetimes.Comment: 12 pages, 3 figure

Gauging of Lorentz Group WZW Model by its Null Subgroup

We consider the standard vector gauging of Lorentz group $SO(3,1)$ WZW model by its non-semisimple null Euclidean subgroup in two dimensions $E(2)$. The resultant effective action of the theory is seen to describe a one dimensional bosonic field in the presence of external charge that we interpret it as a Liouville field. Gauging a boosted $SO(3)$ subgroup, we find that in the limit of the large boost, the theory can be interpreted as an interacting Toda theory. We also take the generalized non-standard bilinear form for $SO(3,1)$ and gauge both $SO(3)$ and $E(2)$ subgroups and discuss the resultant theories.Comment: 11 pages, LaTeX fil

Vector-Chiral Equivalence in Null Gauged WZNW Theory

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, LaTe