An introduction to string theory and its spectrum

1. Introduction. Why string theory? Field-theory amplitudes and UV divergences. A refresher on the Gamma function and its properties. The Veneziano amplitude.

2. Classical strings. From a point particle to the bosonic string. The Nambu-Goto action. The Polyakov action and its symmetries. The classical Virasoro constraints.

3. Quantum strings. Old-covariant quantisation. The Fock space of string states. The level-by-level construction of the string spectrum in the old-covariant way and in the light-cone.

4. Conformal field theory basics. The worldsheet CFT. Vertex operators. The Del Giudice, Di Vecchia, Fubini (DDF) method for the construction of the spectrum.

5. Regge trajectories. A refresher on Young diagrams and polarisations. Howe duality basics. An efficient and covariant technology for the construction of entire subleading Regge trajectories.

6. String amplitudes I. The rudiments of the computation of tree-level string scattering amplitudes using Wick's theorem. The calculation of the Veneziano and of the Virasoro-Shapiro amplitudes.

7. String amplitudes II. The method of the generating functional. The tree-level graviton 3-point amplitude. General Relativity from a low-energy string and string corrections to GR.

8. Superstrings I. The Ramond-Neveu-Schwarz superstring. The fermion CFT. The level-by-level construction of the superstring spectrum.

9. Superstrings II. Howe duality for the superstring. An efficient and covariant technology for the construction of entire subleading Regge trajectories of the superstring.

10. Other topics. A brief introduction to elements of string compactifications, string dualities and the Anti-de-Sitter / CFT correspondence.