Boundary Conformal Field Theory

TL;DR

Boundary conformal field theory (BCFT) studies CFTs with boundaries, offering simpler mathematical structures and significant applications in string theory and condensed matter physics, focusing on foundational quantum field theory concepts.

Contribution

This paper provides an accessible overview of BCFT from a quantum field theory perspective, emphasizing core ideas without delving into specific applications or advanced mathematical frameworks.

Findings

BCFT simplifies the algebraic and geometric structures of CFT.

BCFT has important applications in string theory and condensed matter physics.

The paper clarifies foundational concepts of BCFT in quantum field theory.

Abstract

Boundary conformal field theory (BCFT) is simply the study of conformal field theory (CFT) in domains with a boundary. It gains its significance because, in some ways, it is mathematically simpler: the algebraic and geometric structures of CFT appear in a more straightforward manner; and because it has important applications: in string theory in the physics of open strings and D-branes, and in condensed matter physics in boundary critical behavior and quantum impurity models. In this article, however, I describe the basic ideas from the point of view of quantum field theory, without regard to particular applications nor to any deeper mathematical formulations.