Condições de contorno em AdS CFT: campos escalares e vetoriais

Abstract

The AdS/CFT (anti-de Sitter/conformal field theory) correspondence, proposed by Juan Maldacena in 1997, changes the way we understand gravitational systems and field theory. Precisely it was proposed that an type IIB string theory in low energy (supergravity) defined in AdS₅ ×S⁵ spacetime is equivalent to an conformal field theory N = 4 Super Yang-Mills SU(N) in 4 dimensions. In this work we will explore this correspondence in a simplified way, any quantum field theory in an asymptotically andide Sitter d + 1 spacetime can be mapped to an conformal field theory in its boundary. This map is holographic, it relates the bulk theory with an boundary theory. To define the bulk theory dynamics we need to impose boundary conditions, and because there is more than one way to do it, this information is mapped to the boundary theory. The holographic map can access the information of the boundary conditions. Using this feat we will try to understand this map studying two well know cases, the massive scalar field and the massive gauge field. The first step of this study will be understand the basic concepts of the holographic correspondence. After that we will apply the map to each theory using distinct boundary conditions and, in the end, we will compare them.