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.

1. KK Compactification I.
1. CM and QM on $R^(3,1)x S^1$ and the spectrum of KK theory.
2. KK dimensional reduction on a circle S^1.
1. Scherk-Schwarz formalism.
2. Newton's constant and masses.
3. The full KK theory with massive modes and its symmetries.
4. Sources:
1. Direct KK reduction of the massless particle action.
2. Dimensional reduction of the AS shock-wave spacetime.
3. The extreme electric KK black hole.
2. KK Compactification II.
1. d=4 KK electric-magnetic duality.
1. Symmetry of the theory & solution-generating transformation.
2. The extreme magnetic KK black hole.
3. The KK monopole.
2. Toroidal compactifications.
1. General formalism.
2. Symmetries of the action.
3. Generalized dimensional reduction*
1. General idea/formalism.
2. Examples and counterexamples.
3. Brane interpretation
3. String T Duality.
1. T duality in flat backgrounds: mode expansions and spectrum.
2. T duality in general backgrounds (Buscher's T duality).
1. Bosonic string low-energy effective action (LEEA).
2. KK reduction of the LEEA.
1. Dimensional reduction of the string sigma-model (double and direct).
2. T duality between waves and fundamental strings.
4. Type II String and M Theory Dualities.
1. Type II superstrings.
2. The type IIA and IIB superstrings LEEA.
3. Type IIA versus 11-dimensional SUGRA.
4. Type IIB S duality.
5. Type IIA/B T duality.
6. Generalized dimensional reduction and type II T duality*.
5. Brane Dualities
1. Solitonic, fundamental, KK amd D-branes:
1. Generalities, E-M duals.
2. D-branes from flat-space open string mode expansions and T duality.
3. D-brane effective actions and T duality.
4. Solitonic branes.
2. Solutions and dualities: the general picture.
3. Some uses: d=4 extreme black holes*.

*: If there is enough time.