Course details
Semester
 Autumn 2021
 Monday, October 4th to Friday, December 10th
Hours
 Live lecture hours
 10
 Recorded lecture hours
 0
 Total advised study hours
 40
Timetable
 Thursdays
 12:05  12:55
Course forum
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Description
After motivating the relation between strings and conformal field theories using the Polyakov action, we develop the basic elements of twodimensional 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 spacetime interpretation of the physical string states.
Time permitting we will discuss the dimensional reduction of strings, Tduality, the relation between nonabelian gauge symmetries and KacMoody algebras, and orbifolds.
Prerequisites
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. NambuGoto and Polyakov action. Conformal gauge and conformal invariance.
 Conformal invariance in two dimensions. Witt and Virasoro algebra. Twodimensional conformal field theories.
 Conformal field theory of free bosons and its relation to strings.
 Quantisation of strings using conformal field theory of free bosons. Spacetime 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, KacMoody algebras. Example: Conformal field theory of compact bosons.
 Compactification of strings on a circle. Spectrum, symmetry enhancement. Tduality.
 Orbifolds.
 Outlook
Lecturer

TM
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.
 A Mathematical Introduction to Conformal Field Theory (Martin Schottenloher, book)
 Basic Concepts of String Theory (Ralph Blumenhagen, Dieter Lüst and Stefan Theisen, book)
 Conformal Field Theory (Philippe Francesco, Pierre Mathieu and David Senechal, book)
 Introduction to Conformal Field Theory (Ralph Blumenhagen and Erik Plauschinn, book)
 String Theory: Volume 1, An Introduction to the Bosonic String (Joseph Polchinski, book)
 Superstring Theory (Michael B. Green, John H. Schwarz and Edward Witten, book)
Assessment
The assessment for this course will be released on Monday 10th January 2022 and is due in by Sunday 23rd January 2022 at 23:59.
Assessment for all MAGIC courses is via takehome exam which will be made available at the release date (the start of the exam period).
You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).
If you have kept uptodate with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.
Please note that you are not registered for assessment on this course.
Lectures
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