Aspectos clássicos da teoria de cordas e sua formulação no espaço-tempo de anti-de Sitter 5-dimensional

Abstract

In this work we introduce the main notions of the classical formulation of string theory. We first construct the Nambu-Goto action for strings, motivated by the action of a relativistic point particle. The symmetries of the Nambu-Goto action are analyzed, as well as its equations of motion. We then construct a new action, for mathematical motivations, called Polyakov action, which is classically equivalent to Nambu-Goto action. We explore its equations of motion and its symmetries, acting as gauge transformations and simplifying the action. Furthermore, we demonstrate the existence of a residual symmetry in this action, in addition to the study of general solutions of the equations of motion for strings. We also explore specific examples of a class of solutions, called rigid spinning strings. Finally, we introduce in a simplified way the AdS/CFT correspondence, serving as a motivation to study the dynamics of strings in 5-dimensional anti-de Sitter spacetime (AdS₅). We find two ways to represent AdS5-space, then construct actions for strings in this space-time, moving on to discuss equations of motion, and finally constructing an explicit solution of a spinning rigid circular string on AdS₅ × S⁵.