LMP Seminar (video conference): How string theory emerges from the harmonic oscillator

The Hamiltonian formulation of the one-dimensional harmonic oscillator associates a curve in phase space to a given energy. In terms of complex phase space variables, this curve is a two-dimensional Riemann surface. The Schrödinger equation in the corresponding quantum mechanical problem can be interpreted as a quantization of the curve. The WKB method provides a solution to the equation as a formal asymptotic power series in the Planck constant hbar. Surprisingly, the hbar expansion terms correspond to perturbative loop expansion free energies of a topological string theory. Both the expansion terms as well as the re-summed power series have intriguing mathematical and physical meaning. I will outline this setup as well as its generalizations, which lead to non-perturbative descriptions of gauge theories as well as microstate counting problems of black holes. These are subjects studied by a community of physicists and mathematicians working on the geometry of quantum field and string theories.