A study of string theory and the AdS/CFT correspondence

TL;DR

This work provides a comprehensive, pedagogical synthesis of string theory and the AdS/CFT correspondence, tracing the logic from large-$N$ Yang–Mills to a gauge/gravity duality. It develops the bosonic string as a tractable toy model (conformal gauge, D-branes, open–closed duality) and then elevates the discussion to type II superstrings, where Maldacena's original conjecture situates Type IIB string theory on $AdS_5\times S^5$ in duality with $\mathcal{N}=4$ super-Yang–Mills in four dimensions, via the holographic dictionary. The text emphasizes open–closed duality, D-branes, T-duality, and effective actions (Born–Infeld, DBI, and low-energy supergravity), illustrating how gravity and gauge theories emerge as dual descriptions of the same underlying system. By building from worldsheet conformal field theory to spacetime effective actions, the discussion clarifies how holography arises from string theory's structural features, providing a solid foundation for applications of AdS/CFT to strongly coupled gauge dynamics. The key takeaway is that gauge theories at strong coupling are encoded in weakly coupled gravitational theories in higher dimensions, enabling quantitative insights into nonperturbative phenomena via the holographic correspondence. The explicit, sectioned treatment of historical context, quantization, dualities, and the open/closed sectors makes the holographic dictionary and the role of D-branes central to understanding gauge/gravity duality.

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.

Figures (27)

• Figure 1: Plot of Regge trajectories, taken from Ebert_2009.
• Figure 2: Simplified rigid string model of a meson.
• Figure 3: Gluon field flux tube between a quark and an antiquark, forming a shape similar to a stretched open string between them.
• Figure 4: An open string (a) has two endpoints, represented as dots. A closed string (b) closes in on itself. String theory includes both, but the meson interpretation only holds for the former.
• Figure 5: Three gluon vertex in the double line notation.