Lectures on Branes in Curved Backgrounds

TL;DR

This paper provides an introduction to the microscopic description of branes in curved backgrounds, covering boundary conformal field theory and recent developments in non-compact spaces.

Contribution

It offers a comprehensive overview of boundary conformal field theory techniques applied to branes in curved backgrounds, including recent advances for non-compact target spaces.

Findings

Detailed formalism for branes on compact group manifolds

Review of recent results for non-compact target spaces

Connection between boundary CFT and brane configurations

Abstract

These lectures provide an introduction to the microscopic description of branes in curved backgrounds. After a brief reminder of the flat space theory, the basic principles and techniques of (rational) boundary conformal field theory are presented in the second lecture. The general formalism is then illustrated through a detailed discussion of branes on compact group manifolds. In the final lecture, many more recent developments are reviewed, including some results for non-compact target spaces.