String Theory (MAGIC081)
13 Februar 2017. Marked papers with annotations have been uploaded. Model solutions have been posted under course files. Good work, congratulations! 23 November 2016. Example sheet 3 and solutions to sheet 2 have been posted. We'll probably complete part 5 of the lectures this Thursday. The last two weeks we'll discuss interactions, effective field theories, and compactification. The corresponding part 6 of the lecture notes will be released soon. There will be no example sheet and no assessment for part 6. 13 October 2016. I have posted example sheet 1. You should be able to do Problems 1 and 2 straight away. The material for Problem 3 will be covered in the next lecture. Full solutions will be made available later. I have also already posted Part 3 of the lecture notes, in case we finish Part 2 before the end of the next lecture. 6 October 2016. Parts 1 and 2 of lecture slide, together with some supplementary notes, have been posted.
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 2016 (Monday, October 3 to Friday, December 9)
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
Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will 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.)
MAGIC081 will be assessed by a Take Home Exam during the standard Magic assessment period in January 2017. The exam will consist of four problems, each worth 25 marks. To pass the exam you'll need to obtain a total of 50 marks out of all four problems.
Magic String Assignment
Files marked L are intended to be displayed on the main screen during lectures.
Please log in to view lecture recordings.