MAGIC081: String Theory

Course details

Semester

Autumn 2017
Monday, October 9th to Friday, December 15th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
0

Timetable

Thursdays
12:05 - 12:55

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

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Assessment

The assessment for this course will be released on Monday 8th January 2018 and is due in by Sunday 21st January 2018 at 23:59.

MAGIC081 (String Theory) will be assessed by a single take home exam during the standard MAGIC exam period in January 2018. The exam will consist of four questions, each worth 25 marks. You will need 50 marks to achieve a pass.

Please note that you are not registered for assessment on this course.

Files

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Lectures

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