Introduction to String Theory

Course content

This course gives a basic introduction to string theory. It begins with an introduction to classical string theory and the covariant quantization of the closed string. Then it proceeds to strings in background fields, branes as higher-dimensional objects, quantization of the open string and D-branes, and superstring theory.


MSc Programme in Physics

Learning outcome

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 covers strings in background field, enabling one to get general relativity from string theory, branes as extended objects in higher-dimensional space-times, open strings and D-branes and superstring theory.


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 strings propagating in non-trivial backgrounds.
  • 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 the massless spectrum of closed superstrings.
  • Be able to explain the essentials of T-duality for type IIA and type IIB string theory.


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.

Lectures and exercises

Lecture notes by Troels Harmark

Good knowledge of quantum mechanics, classical mechanics and special relativity. Some knowledge of General Relativity and Cosmology and Elementary Particle Physics at M.Sc. level. It can be beneficial (but it is not necessary nor required) to take it at the same time as Quantum Field Theory I.

Academic qualifications equivalent to a BSc degree is recommended.

Offered every second year.

7,5 ECTS
Type of assessment
Oral examination, 30 minutes
Type of assessment details
No preparation time
Without aids
Marking scale
7-point grading scale
Censorship form
No external censorship
Exam period

Several internal examiners.


same as regular exam

Criteria for exam assessment

see learning outcome

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 35
  • Preparation
  • 149,5
  • Exercises
  • 21
  • Exam
  • 0,5
  • English
  • 206,0


Course number
7,5 ECTS
Programme level
Full Degree Master

1 block

Block 4
No restrictions
Study Board of Physics, Chemistry and Nanoscience
Contracting department
  • The Niels Bohr Institute
Contracting faculty
  • Faculty of Science
Course Coordinator
  • Troels Harmark   (7-6c65767165766f4472666d326f7932686f)
Saved on the 28-02-2023

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