Outline of the course:
1. M-theory as a supersymmetric theory in 11 dimensions. Super Poincare symmetry, central extensions, M-theory superalgebra.
2. 1/2 BPS objects in eleven dimensions: supergravitons, M2-branes, M5-branes. Their approximate description by solutions of 11d supergravity. Lift of the Type IIA D6-brane to 11 dimensions, as a Kaluza-Klein monopole; the D6-brane charge in M-theory superalgebra. Example of compactifications via the superalgebra: Type IIA and M-theory on the circle.
3. Further reduction of supersymmetry in uncompactified spacetime: 1/4 BPS objects, bound states. Discussion of examples of supergravity solutions with exotic fractions of supersymmetry.
4. Worldvolume theory of M5-branes; little string theories.
5. Worldvolume theory of M2-branes, analogies with the Green-Schwarz formulation of Type II superstrings. Physical gauge, lightcone gauge. Cohomological interpretation of the Wess-Zumino term on the worldvolume of supersymmetric branes.
6. Low-energy supergravity in 11 dimensions.
7. Spacetime boundaries, heterotic M-theory. Anomalies and the boundary E_8 super Yang-Mills multiplet. Effective low-energy action on manifolds with boundaries.
8. Anomalies in 10d superstring theories, Type IIB anomaly cancellation, the Green-Schwarz mechanism in heterotic/Type I theory, relation to modular invariance.
9. Compactification on tori. Reducing supersymmetry by compactification: M-theory on special holonomy manifolds. Web of M-theory/string theory dualities. Example: M-theory on K3 / heterotic on T^3.
10. Compactifications on Calabi-Yau; compactifications of heterotic strings and heterotic M-theory to four dimensions with N=1 supersymmetry.
11. Elements of Matrix theory.
12. Elements of AdS/CFT correspondence.
13. More on compactifications: Mirror symmetry, heterotic/heterotic dualities, etc.
14. Braneworlds, supersymmetry breaking and stability, cosmology.
horava@socrates.berkeley.edu