MAGIC081: String Theory

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

Visit the MAGIC081 forum

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. 

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. 

Syllabus

  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 

Lecturer

  • TM

    Thomas Mohaupt

    University
    University of Liverpool

Bibliography

No bibliography has been specified for this course.

Assessment

Attention needed

Assessment information will be available nearer the time.

Files

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Lectures

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