- Generalize the mass-shell condition (Klein-Gordon equation in momentum space) by using the Dirac equation.
- The gamma matrices will serve as CM modes of an anticommuting world sheet field.
- The resulting world-sheet supercurrents generate the superconformal transformations of the superconformal algebra.
- Counting the number of (3/2, 0) currents classifies the different superconformal field theories.
- Standard quantization techniques for constrained systems are applied.
- Free SCFTs can be obtained with the vanishing of the central charge giving 10 as the critical dimension.
- SCFT on a circle gives two periodicity conditions for the matter fermions (Ramond and Neveu-Schwarz sectors).
- Ramond and Neveu-Schwarz algberas result. - Holomorphicity constraints give bosonization via the relation between the R sector vertex operators and bosonic winding state vertex operators.
- In 10 flat dimensions, 16 sectors result from the R and NS sectors, 6 of which are empty.
- Consistency conditions yield type IIA and IIB superstring theories.
- The vacuum amplitude for a closed superstring can be found by imposing modular invariance.
- Divergences cancell in the cylinder, Mobius strip, and Klein bottle graphs.
- Generalize preceding constructions by looking for sets of holomorphic and antiholomorphic currents whose Laurent coefficients form a closed algebra.
- Consider algebras that are different on the left- and right-moving sides of the closed string, obtaining the heterotic string.
- Setting the dimensions to be the same at each side and 32 left-moving spin-1/2 fields gives the SO(32) string.
- Split these fields into sets of 16 with independent boundary conditions to get the E8 X E8 heterotic string.
- Use supersymmetry constraints to study interactions of massless degrees of freedom.
- Tree-level interactions can be studied within low-energy supergravity; one-loop gives rise to anomalies.
- Anomalies cancell in type IIA, IIB, type I, and heterotic string theories.
- Use string perturbation theory to calculate amplitudes and interactions.
- Introduce supersymmetry in toroidally compactified string theory, to obtain D-branes which are BPS states and carry R-R charges.
- Type I, IIA, IIB string theories become states in a single theory.
- Study strongly coupled strings using D-brane states.
- The five string theories are limits of a single theory in 11-dimensional spacetime.
- Study conformal field theories as a prolegomena to analyzing string compactification.
- Study string compactification via free world-sheet conformal field theories or interacting exactly solvable conformal field theories.
- Connect the compactified string theory to the Standard Model.
- Start with orbifolds and then the more general Calabi-Yau manifolds.
- Techniques from algebraic geometry are brought in to study the properties of Calabi-Yau manifolds.
- Deduce an effective (low-energy) four-dimensional action using the topology of Calabi-Yau manifolds.
- Elaborate on the physics of four-dimensional string theory.
- Try to deal with the strong CP problem using Peccei-Quinn symmetry and the resulting axion field.
- Try to understand how gauge symmetries arise in the different string theories and how they are related to the ones in the Standard Model.
- Try to connect the different mass scales in string theory.
- Study more advanced topics in string theory, such as N = 2 superconformal algebras, type II superstrings on Calabi-Yau manifolds, string theories on the 4-dimensional Calabi-Yau manifold K3, minimal models, and mirror symmetry.
- Mirror manifolds can be constructed explicitly using Gepner models.
- Use mirror symmetry to obtain the full low energy field theory at the string tree level.
- Flop transitions can occur in string theory, giving dynamical changes in topology.
