Course details
Semester
 Autumn 2024
 Monday, October 7th to Friday, December 13th
Hours
 Live lecture hours
 10
 Recorded lecture hours
 0
 Total advised study hours
 40
Timetable
 Thursdays
 13:05  13:55 (UK)
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
Dr Thomas Mohaupt
 University
 University of Liverpool
Bibliography
No bibliography has been specified for this course.
Assessment
The assessment for this course will be released on Monday 13th January 2025 at 00:00 and is due in before Friday 24th January 2025 at 11:00.
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 hoursâ€™ work to attain the pass mark, which is 50%.
Please note that you are not registered for assessment on this course.
Files
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Lectures
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