يادداشتي به دوگاني ADS/CFT

Note on AdS/CFT duality

We study duality of field theories in (d+1) dimensional flat Euclidean space and (d+l) dimensional Euclidean AdS space for both scalar the and vector fields. In the case of the scalar theory, the injective map between conformally coupled massless scalars in two spaces is reviewed. It is shown that for vector fields the injective map exists only in four dimensions. Since Euclidean AdS space is equivalent to half flat Euclidean space up to a conformal map, using the injective maps, we interpret AdS/CFT duality as a correspondence between solutions of equation of motion and the corresponding Cauchy data.