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We give an introduction to string theory with emphasis on its relation to two-dimensional conformal field theories. After motivating the relation between strings and conformal field theories using the Polyakov action, we develop the basic elements of two-dimensional conformal field theories, and illustrate them using the special case of the theory of free bosons. We use this example to explain the quantisation of strings in the conformal gauge and provide the space-time interpretation of the physical string states. Time permitting we will discuss the dimensional reduction of strings, T-duality, the relation between non-abelian gauge symmetries and Kac-Moody algebras, and orbifolds.


Autumn 2019 (Monday, October 7 to Friday, December 13)


  • Live lecture hours: 10
  • Recorded lecture hours: 0
  • Total advised study hours: 40


  • Thu 12:05 - 12:55


A good working knowledge of quantum mechanics and special relativity is assumed. Basic knowledge in quantum field theory, general relativity, group theory and differential geometry is helpful.


1) Action principles for relativistic particles. 2) Action principles for relativistic strings. Nambu-Goto and Polyakov action. Conformal gauge and conformal invariance. 3) Conformal invariance in two dimensions. Witt and Virasoro algebra. Two-dimensional conformal field theories. 4) Conformal field theory of free bosons and its relation to strings. 5) Quantisation of strings using conformal field theory of free bosons. Space-time interpretation of states. Momentum and angular momentum. Null states and gauge symmetries. 6) Analysis of physical states. Examples of physical states: Tachyon, photon, antisymmetric tensor, graviton, dilaton. Elements of the representation theory of the Poincare group. 7) Conformal field theories with extended symmetries, Kac-Moody algebras. Example: Conformal field theory of compact bosons. 8) Compactification of strings on a circle. Spectrum, symmetry enhancement. T-duality 9) Orbifolds. 10) Outlook

Other courses that you may be interested in:


Thomas Mohaupt
Phone 0151 7955177
Photo of Thomas Mohaupt


Basic Concepts of String TheoryBlumenhagen, Lüst and Theisen
Introduction to Conformal Field Theory: With Applications to String TheoryBlumenhagen and Plauschinn


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The course will be assessed by an assignment during the standard MAGIC exam period. The assignment will consist of four problems, each worth 25 marks. You'll need at least 50 marks to pass.

Magic 081 String Theory Assignment January 2020

Files:Exam paper
Released: Monday 6 January 2020 (184.5 days ago)
Deadline: Sunday 19 January 2020 (170.5 days ago)

Answer all questions. Each of the four questions carries 25% of the marks. You need 50% to pass.

Recorded Lectures

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