An Introduction to Extra Dimensions.pdf

a r X i v : h e p - p h / 0 5 0 3 1 7 7 v 2 3 0 M a y 2 0 0 5 An Introduction to Extra Dimensions ? Abdel Pe?rez-Lorenzana Departamento de F??sica, Centro de Investigacio?n y de Estudios Avanzados del I.P.N. Apdo. Post. 14-740, 07000, Me?xico, D.F., Me?xico (Dated: February, 2005) Models that involve extra dimensions have introduced completely new ways of looking up on old problems in theoretical physics. The aim of the present notes is to provide a brief introduction to the many uses that extra dimensions have found over the last few years, mainly following an effective field theory point of view. Most parts of the discussion are devoted to models with flat extra dimensions, covering both theoretical and phenomenological aspects. We also discuss some of the new ideas for model building where extra dimensions may play a role, including symmetry breaking by diverse new and old mechanisms. Some interesting applications of these ideas are discussed over the notes, including models for neutrino masses and proton stability. The last part of this review addresses some aspects of warped extra dimensions, and graviton localization. I. INTRODUCTION: WHY CONSIDERING EXTRA DIMENSIONS? Possible existence of new spatial dimensions beyond the four we see have been under consideration for about eighty years already. The first ideas date back to the early works of Kaluza and Klein around the 1920’s [1], who tried to unify electromagnetism with Einstein gravity by proposing a theory with a compact fifth dimension, where the photon was originated from the extra components of the metric. In the course of the last few years there has been some considerable activity in the study of models that involve new extra spatial dimensions, mainly motivated from theories that try to incorporate gravity and gauge interactions in a unique scheme in a reliable manner. Extra dimensions are indeed a known fundamental ingredient for String Theory, since all versions of the theory are naturally and