String Theory (MAGIC081) |
GeneralDescription
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.
SemesterAutumn 2019 (Monday, October 7 to Friday, December 13) Hours
Timetable
PrerequisitesA 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.
Syllabus1) 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
Bibliography
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