PSI 2017/2018 - String Theory (Gaiotto)

General considerations on string theory: perturbative string theory, D-branes, Dualities.

 Path integral for a scalar field; Strings: Nambu Goto action, Polyakov action, Weyl symmetry, gauge fixing, Riemman surface, critical string.

The two-dimensional free boson: mode expansion, fock space; symmetries; the stress energy tensor and the Virasoro algebra.

The string spectrum.

Ghosts and other terrors - BRST gauge fixing.

Ghosts in string theory - BRST-symmetric path integral for a bosonic string.

Ghost Hilbert space - BRST cohomology.

State-Operator map: general states in the free boson Hilbert space - ghost; Sphere correlation function; Scattering amplitude A_{TTT}. 

Scattering amplitude A_{TTTT}.

Propagation of string in curved space - String theory effective action from 2d RG flow -Kaluza-Klein compactification - T-duality.

Branes - Neumann and Dirichlet boundary conditions.

Introduction to superstrings - example of a supersymmetric quantum mechanics system.