IJUP08 - Universidade do Porto

Anti-de Sitter space and the stability of scalar field
C. A. dos Santos Guedes 1
1 Department of Physics, Faculty of Sciences, University of Porto, Portugal.
This work grew up as an introduction to what I have been doing in my final undergraduate
thesis, a purely theoretical physics research based on what is called the AdS/CFT duality,
under the supervision of Dr. Miguel da Sousa Costa.
AdS stands for anti-de Sitter space which is a solution to Einstein’s field equations of
general relativity in empty space with negative cosmological constant. Being a maximally
symmetric space, it has been an excellent model to investigate questions of principle
related to the quantization of fields propagating on curved background, the interaction with
the gravitational field and the issues related to its lack of global hyperbolicity.
Firstly, I focused on the geometric properties of anti-de Sitter and understood how subtle
this space is, where time warps in itself and light reaches the spatial infinity in finite time.
Moreover the symmetries, or the group to which this space is invariant, induce a natural
behavior on its boundary that is conformally invariant. CFT above denotes conformal field
theory.
Afterwards, I delved into the propagation of scalar field. The scalar field corresponds in
real world to what we can think of spinless particles (spin is an intrinsic property of
particles like mass and charge). For us to have particles they must be stable to the extent
that we can manipulate them in a consistent way, i.e., be able to do quantum field theory.
This part was based on work done almost thirty years ago [1-3], which led to the
conclusion that the scalar field is stable in any dimension for an AdS fixed background.
Because the mathematical apparatus and concepts used are far from being trivial, and the
audience is a very general one, the main part of the presentation will be concerned with
very general ideas about what General Relativity, Quantum Mechanics and Quantum Field
Theory is all about and why it is important to think of them from a unified point of view. If
time permits, further questions specific to this work could be addressed.
References:
[1] Breitenlohner, P. and Freedman, D. Z. (1982), Positive Energy in Anti-de Sitter Background
and Gauged Extended Supergravity, Phys. Lett. B 115.
[2] Breitenlohner, P. and Freedman, D. Z. (1982), Stability in Gauged Extended Supergravity, Ann.
Phys. 144.
[3] Mezincescu, L., and Townsend, P. K. (1985), Stability at a Local Maximum in Higher
Dimensional Anti-de Sitter Space and Applications to Supergravity, Ann. Phys. 160.
38