A study of string theory and the AdS/CFT correspondence

TL;DR

This paper provides a comprehensive review of string theory and the AdS/CFT correspondence, explaining their foundations, key concepts, and the holographic duality, aimed at pedagogical understanding.

Contribution

It offers a detailed, pedagogical derivation of the AdS/CFT correspondence and explores core string theory topics relevant to this duality, including D-branes and superstring theories.

Findings

Derivation of the AdS/CFT correspondence

Analysis of D-branes via T-duality

Matching spectra of superstring theories and supergravity

Abstract

This dissertation consists of a comprehensive and pedagogical review of Maldacena's original derivation of the AdS/CFT correspondence and the main topics of string theory necessary to understand it. The large $N$ expansion of Yang-Mills theory is presented as the main motivation for seeking a string-theoretic language for gauge theories. The bosonic string is studied in conformal gauge, with an emphasis on the spectrum and the low energy effective actions for both closed and open strings. The properties of D-branes are studied via T-duality, and closed-open string duality is checked by explicitly computing the interaction amplitude between two D-branes. The type II superstring theories are studied in the RNS formalism and their massless spectrum is shown to match that of the type II ten-dimensional supergravity theories. Supersymmetric branes are discussed, including their realization as supergravity solitons, and the original derivation of the AdS/CFT duality is presented. Some of the properties of the correspondence are discussed, including the idea of the holographic dictionary.