Course Information for 
Physics 7910/String Theory

Contents

Class Meetings

Course Description

This is an introductory course on String Theory. Basic topics as well as modern research will be covered. After an introduction we will be discussing the bosonic string. The reason why bosonic string theories can only live in 26 dimensions and the spectrum of the bosonic string will be discussed. The world-sheet quantum field theory that describes the bosonic string is a conformally invariant quantum field theory in two dimensions. Therefore an introduction to conformal field theory will be given. Beyond its importance in string theory, conformal field theories also found applications in statistical physics and condensed matter physics. Then we will be discussing the supersymmetric string theories. After a general introduction of supersymmetry we will be discussing string theories with a world-sheet supersymmetry. Space-time supersymmetry and the 5 consistent string theories will the be the subject of the next classes. These theories are only consistent in ten dimensions. But there is no need that all ten dimensions be infinitely extended. In order to make contact between string theory and the real world six of the dimensions can be small and compact while the four additional dimensions are infinitely extended and represent our world. Unbroken supersymmetry imposes conditions on the internal manifold. One type of internal manifolds that satisfies these conditions are Calabi-Yau manifolds. These manifolds will be discussed in detail as well as the corresponding phenomenology. If superstrings describe nature then they have to incorporate non-abelian gauge symmetries. On way to obtain non-abelian gauge symmetries is by considering type I and heterotic string theories. These theories will be discussed in detail. Nowadays it has been understood that the five apparently different string theories that live in ten dimensions can actually be derived from an eleven-dimensions theory called M-theory. An introduction to M-theory will be given. Then we will be discussing string dualities and D-branes. If timing allows it we will be discussing further modern developments in string theory.

Instructor

Course Requirements

Prerequisites

Certainly it would be useful to have had a previous course on quantum mechanics. It would also be useful to know something about special relativity and have some basic knowledge of general relativity. We will use some rudimentary group theory and differential forms. But we will review this material when we get to it, so you don't need to worry if you haven't seen it before.

References

• ``Superstring Theory'' Volumes 1 and 2, by Green, Schwarz and Witten, Cambridge University Press.


• ``String Theory'' Volumes 1 and 2, by Polchinski, Cambridge University Press.

• Introduction to Superstring Theory, by E. Kiritsis.
• An Introduction to Non-Perturbative String Theory, by A. Sen.
• Introduction to Superstring Theory, by J. H. Schwarz.
• TASI Lectures on D-branes, by J. Polchinski.

Course Outline

• 6 January - 15 January (2 weeks):
  Motivation of string theory and discussion of the bosonic string.

• 22 January - 27 January (1 week):
  Conformal field theory.

• 29 January - 3 February (1 week):
  Introduction to global and local supersymmetry.

• 5 February - 10 February (1 week):
  Strings with wold-sheet supersymmetry.

• 12 February - 19 February (1 week):
  Strings with space-time supersymmetry.

• 24 February - 26 February (1 week):
  Type I and type II strings.

• 3 March - 5 March (1 week)
  Non-abelian gauge symmetry and open strings.

• 10 March - 12 March (1 week):
  Heterotic strings.

• 24 March - 26 March (1 week):
  Low-energy effective actions of string theory and eleven-dimensional supergravity.

• 31 March - 2 April (1 week):
  Calabi-Yau compactifications.

• 7 April - 14 April (1+1/2 weeks):
  Open Strings and D-branes.

• 16 April - 21 April (1 week):
  M-theory.

Last modified: Jan 10, 2003.