Introduction to String Theory

Knowledge
The course will begin with an introduction to the action description of classical relativistic strings, including discussion of symmetries, constraints and action principle. The course then turns to quantization of closed bosonic string theory using covariant quantization, discussing anomalies versus symmetries in quantized theories and the critical space-time dimension. Subsequently, the course will cover D-branes, as extended objects from open strings, and superstring theory. Finally, it will be reviewed how the AdS/CFT correspondence is a consequence of superstring theory.

Skills

At the end of the course, the student is expected to:

• Be able to write down and use the Nambu-Goto and Polyakov actions for classical relativistic strings.
• Be able to quantize the open and closed bosonic string and compute the spectrum.
• Be able to explain classical conformal symmetry, its quantum version with Virasoro algebras, and how this is connected to the covariant quantization of the closed string. 
• Be able to explain the connection between the critical space-time dimension of string theory and anomalies in the conformal symmetry in two dimensions.
• Be able to understand the main elements of how general relativity arise from string theory.
• Be able to explain how a D-brane is defined from open string theory.
• Be able to explain branes as higher-dimensional objects in higher-dimensional space-times, including branes with charges, and use this for understanding the description of D-branes and the fundamental string.
• Be able to understand the essentials of generalizing the bosonic string to the superstring and to show that the world-sheet action for superstrings is supersymmetric.
• Be able to explain how the AdS/CFT correspondence is a consequence of superstring theory

Competences
This course builds on the of knowledge quantum mechanics, special and general relativity. The course will provide the students with a competent background for further studies within this research field, i.e. a M.Sc. project in theoretical high energy physics. It will also provide those that plan to continue into experimental high energy physics or cosmology the necessary background to understand the physics of string theory.
This course will provide the students with mathematical tools that have application in a range of fields within and beyond physics.