Course details
A specialist MAGIC course
Semester
- Autumn 2020
- Monday, October 5th to Friday, December 11th
Hours
- Live lecture hours
- 10
- Recorded lecture hours
- 0
- Total advised study hours
- 40
Timetable
- Thursdays
- 12:05 - 12:55 (UK)
Description
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.
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.
Prerequisites
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.
Basic knowledge in quantum field theory, general relativity, group theory and differential geometry is helpful.
Syllabus
- Action principles for relativistic particles.
- Action principles for relativistic strings. Nambu-Goto and Polyakov action. Conformal gauge and conformal invariance.
- Conformal invariance in two dimensions. Witt and Virasoro algebra. Two-dimensional conformal field theories.
- Conformal field theory of free bosons and its relation to strings.
- Quantisation of strings using conformal field theory of free bosons. Space-time interpretation of states. Momentum and angular momentum. Null states and gauge symmetries.
- Analysis of physical states. Examples of physical states: Tachyon, photon, antisymmetric tensor, graviton, dilaton. Elements of the representation theory of the Poincare group.
- Conformal field theories with extended symmetries, Kac-Moody algebras. Example: Conformal field theory of compact bosons.
- Compactification of strings on a circle. Spectrum, symmetry enhancement. T-duality.
- Orbifolds.
- Outlook
Lecturer
-
Dr Thomas Mohaupt
- University
- University of Liverpool
Bibliography
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.
- Introduction to Conformal Field Theory: With Applications to String Theory (Blumenhagen and Plauschinn, book)
- A first course in string theory (B. Zwiebach, book)
- Basic Concepts of String Theory (Ralph Blumenhagen, Dieter Lüst and Stefan Theisen, book)
- D-Branes (Clifford V. Johnson, book)
- String Theory and M-Theory (Katrin Becker, Melanie Becker and John H. Schwarz, book)
- String Theory: Volume 1, An Introduction to the Bosonic String (Joseph Polchinski, book)
- Superstring Theory (Michael B. Green, John H. Schwarz and E. Witten, book)
Assessment
The assessment for this course will be released on Monday 11th January 2021 at 00:00 and is due in before Sunday 24th January 2021 at 23:59.
Open book exam during the standard Magic semester 1 assessment period. 4 questions, worth a total of 100 marks. Each individual question is worth at least 20 and at most 30 marks. Pass mark is 50 marks.
Please note that you are not registered for assessment on this course.
Files
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Lectures
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