**A Pedagogical Introduction to Kaluza-Klein
Compactifications and Dualities in the Low Energy String Effective
Action**

### Program:

To be given in 5 1.5 hour sessions.

** KK Compactification I.**
- CM and QM on $R^(3,1)x S^1$ and the spectrum
of KK theory.
- KK dimensional reduction on a circle
S^1.
- Scherk-Schwarz formalism.
- Newton's constant and masses.

- The full KK theory with massive modes and its symmetries.
- Sources:
- Direct KK reduction of the massless particle action.
- Dimensional reduction of the AS shock-wave spacetime.
- The extreme electric KK black hole.

**KK Compactification II.**
- d=4 KK electric-magnetic duality.
- Symmetry of the theory & solution-generating transformation.
- The extreme magnetic KK black hole.
- The KK monopole.

- Toroidal compactifications.
- General formalism.
- Symmetries of the action.

- Generalized dimensional reduction*
- General idea/formalism.
- Examples and counterexamples.
- Brane interpretation

**String T Duality.**
- T duality in flat backgrounds: mode expansions and spectrum.
- T duality in general backgrounds (Buscher's T duality).
- Bosonic string low-energy effective action (LEEA).
- KK reduction of the LEEA.
- Dimensional reduction of the string sigma-model (double
and direct).
- T duality between waves and fundamental strings.

**Type II String and M Theory Dualities.**
- Type II superstrings.
- The type IIA and IIB superstrings LEEA.
- Type IIA versus 11-dimensional SUGRA.
- Type IIB S duality.
- Type IIA/B T duality.
- Generalized dimensional reduction and type II T duality*.

**Brane Dualities**
- Solitonic, fundamental, KK amd D-branes:
- Generalities, E-M duals.
- D-branes from flat-space open string mode expansions and T duality.
- D-brane effective actions and T duality.
- Solitonic branes.

- Solutions and dualities: the general picture.
- Some uses: d=4 extreme black holes*.

*: If there is enough time.

Tomás Ortín Miguel
Last modified: Thu Nov 6 06:49:11 CET 2003