A Correspondence Between Supersymmetric Yang-Mills and Supergravity Theories

TL;DR

This paper explores the AdS/CFT correspondence linking supersymmetric gravity in Anti-de-Sitter space with supersymmetric Yang-Mills theory, explaining its significance, origins, and supporting arguments.

Contribution

It provides a comprehensive overview of the AdS/CFT correspondence, including historical context, key concepts like D-branes, and the main arguments supporting this duality.

Findings

Establishes a theoretical link between SUGRA and SYM theories.

Highlights the role of D-branes in the correspondence.

Discusses the significance of the AdS/CFT duality in theoretical physics.

Abstract

AdS/CFT-correspondence establishes a relationship between supersymmetric gravity (SUGRA) on Anti-de-Sitter (AdS) space and supersymmetric Yang-Mills (SYM) theory which is conformaly invariant (CFT). The AdS space is the solution of the Einstein-Hilbert equations with a constant negative curvature. Why is this relationship important? What kind of relationship is this? How does one find it? The purpose of this text is to answer these questions. We try to present the main ideas and arguments underlying this relationship, starting with a brief sketch of old string theory statements and proceeding with the definition of D-branes and a description of their main features. We finish with the observation of the correspondence in question and the arguments that favor it.