Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

Introduction to String Theory

Practical information
Study year 2016/2017
Block 3
Programme level Full Degree Master
Course responsible
  • Troels Harmark (7-7b74858074857e5381757c417e8841777e)
  • The Niels Bohr Institute
Course number: NFYK14014U

Course content

This course gives a basic introduction to string theory. The first part of the course is an introduction to classical string theory and quantized bosonic string theory. The second part of the course is an introduction to conformal invariance, superstring theory and strings in background fields, as well as to related topics.

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 quantized bosonic string theory, with closed and open strings, lightcone quantization, covariant quantization, anomalies versus symmetries in quantized theories, the critical space-time dimension and definition of D-branes. Furthermore, the course will cover conformal symmetry of string theory and it is implemented for the covariant quantization of the bosonic string. Finally, it will cover the more advanced topics of superstrings and strings in background fields.



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 the connection between the critical space-time dimension of string theory and anomalies, both for the lightcone as well as for the covariant quantization.
  • Be able to explain how a D-brane is defined from open string theory.
  • Be able to explain the connection between conformal symmetry in two dimensions, covariant quantization with ghost fields, and the critical space-time dimension.
  • Be able to show that the world-sheet action for superstrings is supersymmetric.
  • Be able to understand the main elements of strings propagating in non-trivial backgrounds.
  • Be able to understand the essentials of generalizing the bosonic string to the superstring.
  • Be able to explain the essentials of why there are five consistent superstring theories.
  • 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.

Recommended prerequisites

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

Mandatory prerequisites

General Relativity and Cosmology.
Elementary Particle Physics.

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MSc Programme in Physics


Study Board of Physics, Chemistry and Nanoscience

Course type

Single subject courses (day)


1 block


---- SKEMA LINK ----

Teaching and learning methods

Lectures and exercises


No restrictions




to be announced


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

Exam (30 minutes oral exam)

Type of assessment

Oral examination, 30 minutes
Oral exam, 30 minutes, no preparation time

Marking scale

7-point grading scale

Criteria for exam assessment

The highest mark (12) is given for excellent exam performance that demonstrates full mastery of the above mentioned learning goals with no or only minor gaps.

The mark 2 is given to a student who has only minimally achieved the course goals

Censorship form

No external censorship

Exam period

Several internal examiners.


same as regular exam

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