Introduction to String Theory
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
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 minutesNo preparation time
- Without aids
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Criteria for exam assessment
see learning outcome
Single subject courses (day)
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
- Block 4
- No restrictions
The number of seats may be reduced in the late registration period
- Study Board of Physics, Chemistry and Nanoscience
- The Niels Bohr Institute
- Faculty of Science
- Troels Harmark (7-6c65767165766f4472666d326f7932686f)
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Courseinformation of students