String Theory (MAGIC081)
The original assessment file contained a typo in problem 2 (the phi_m - phi_n commutator had a wrong coefficient). This has been corrected. Thanks to Viktor Matyas for pointing this out.
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 2018 (Monday, October 8 to Friday, December 14)
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.)
The exam consists of four questions, which will be similar to the example sheets. Each question carries 25 marks. 50 marks are required to pass the exam.
Magic 081 String Theory Assignment January 2019
Files marked L are intended to be displayed on the main screen during lectures.
Please log in to view lecture recordings.