MAGIC081: String Theory

Course details


Autumn 2013
Monday, October 7th to Saturday, December 14th


Live lecture hours
Recorded lecture hours
Total advised study hours


12:05 - 12:55


3 February 2014. I have uploaded all marked exams. All submitted work was very good or excellent. I have made some remarks on the scripts, and posted my model solutions among the course files. Well done!
14 December 2013. Posted: Additional notes for lecture 10, solutions for example sheet 3.
4 December 2013. Posted: Revised version of Part 5 of the lecture notes (some typos fixed), additional notes for lecture 9, solutions for example sheet 2, and example sheet 3.
2 December 2013. Please note that due to local industrial action it is not clear whether I will be able to enter the department and the Magic room on Wednesday 4 December. I will not be on strike myself on this day, but since part of the technical personal will be, it might happen that the departmental building will be closed due to health and safety reasons. If the lecture will not take place, I will make an announcement about how we will proceed as soon as possible. Thank you for your understanding.
30 November 2013. Part 5 of the lecture notes and additional (handwritten notes) for the lectures up to lecture 8 have been posted.
12 November 2013. Part 4 of the lecture notes have been posted. We will start with this during tomorrows lectures and spend up to two further lectures on this material.
12 November 2013. Example Sheet 2 has been posted. Solutions will be made available in about 3 weeks.
12 November 2013. Solutions for Example Sheet 1 have been posted.
7 November 2013. Additional (scanned, handwritten) notes for forth and fifth lecture have been uploaded.
27 October 2013. Part 3 of the lecture notes has been posted.
24 October 2013. I have now posted the additional (scanned, handwritten) notes from the third lecture. I have also posted the first example sheet. Solutions will be made available later (in about 2 weeks). On Wednesday 30 November I will finish the second part of the lectures, and start with part 3. I expect that I'll post the lecture notes for part 3 by Monday 28.
I have now posted (scanned, hand-written) notes from the second lecture. It includes the bibliographic data for the book by Jost which was mentioned in the QandA at the end. Next Wednesday (23 October) we will continue with Part 2 of the lecture notes from page 15.
The second part of the Lecture Notes has been posted. They cover the Nambu-Goto and Polyakov action principles for relativistic (bosonic) strings, the equations of motion and constraints, conserved quantities, explicit solutions of the equations of motion in the conformal gauge and an outline of covariant quantisation. I expect that we will need at least two weeks to go through this material (Lectures 2 and 3).
I have also posted some supplementary (scanned, hand-written) notes from the first lecture.


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.


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


  • TM

    Thomas Mohaupt

    University of Liverpool


Follow the link for a book to take you to the relevant Google Book Search page

You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library' - this sometimes works well, but not always - you will need to enter your location, but it will be saved after you do that for the first time.



The course will be assessed by a single take home exam in January with 2 weeks to complete and submit online. The exam will consist of 6 questions, each worth 25 marks. Only the best 4 answers will be counted. You need 50 marks to pass the exam. There will be 2 problems related to part 2 (relativistic string), 3 problems related to parts 3 4 (conformal field theory, 1 problem related to part 5 (physical states).

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