String theory and conformal field theory (CFT) are closely related concepts in theoretical physics, particularly in the study of quantum field theory and high-energy physics. Here's an overview of their relationship:
Conformal Field Theory (CFT): CFT is a quantum field theory that possesses a special symmetry called conformal symmetry. Conformal symmetry relates to the preservation of angles at every point in a space or spacetime, without any preferred scale. This symmetry plays a fundamental role in various areas of physics, such as critical phenomena, statistical mechanics, and the study of phase transitions.
String Theory: String theory is a theoretical framework that aims to provide a unified description of all fundamental particles and forces in nature. According to string theory, particles are not considered as point-like objects but as tiny, one-dimensional strings. These strings vibrate at different frequencies, giving rise to various particles. String theory is an attempt to reconcile general relativity (describing gravity) with quantum mechanics (describing the behavior of particles on a microscopic scale).
Now, the connection between string theory and conformal field theory arises in the following ways:
Worldsheet Conformal Field Theory: In string theory, the dynamics of the strings is described on a 2-dimensional surface called the worldsheet. The behavior of strings on the worldsheet is governed by a conformal field theory. This conformal field theory describes the quantum properties of the strings and the interactions between them. Therefore, CFT provides the mathematical framework for analyzing the behavior of strings.
AdS/CFT Correspondence: The AdS/CFT correspondence, also known as the gauge/gravity duality or holographic principle, is a profound duality in theoretical physics. It establishes a relationship between string theory in a certain Anti-de Sitter (AdS) spacetime and a conformal field theory living on the boundary of that spacetime. This duality allows researchers to study certain strongly interacting quantum field theories by analyzing the corresponding weakly coupled gravitational theories in higher dimensions. It provides valuable insights into the nature of quantum gravity and the behavior of strongly coupled systems.
In summary, string theory utilizes conformal field theory as the mathematical framework to describe the behavior of strings on their 2-dimensional worldsheet. Additionally, the AdS/CFT correspondence establishes a deep connection between string theory in a specific spacetime and a conformal field theory living on its boundary, enabling the study of strong interactions using gravitational theories.