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


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.

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