Lectures on 2D gravity and 2D string theory (TASI 1992)

TL;DR

This collection of lectures provides an in-depth overview of 2D gravity and string theory, focusing on the c=1 model, matrix models, and continuum approaches, highlighting both theoretical foundations and computational techniques.

Contribution

It offers a comprehensive synthesis of 2D quantum gravity and string theory, integrating conformal field theory, matrix models, and continuum methods with new insights into the c=1 case.

Findings

Analysis of loop and state structures in 2D quantum gravity

Development of matrix model techniques for 2D surfaces

Insights into string scattering in two dimensions

Abstract

Emphasis is on 2d target space (c=1 coupled to gravity). Contents: 0. Introduction, Overview, and Purpose 1. Loops and States in Conformal Field Theory 2. 2D Euclidean Quantum Gravity I: Path Integral Approach 3. Brief Review of the Liouville Theory 4. 2D Euclidean Quantum Gravity II: Canonical Approach 5. 2D Critical String Theory 6. Discretized surfaces, matrix models, and the continuum limit 7. Matrix Model Technology I: Method of Orthogonal Polynomials 8. Matrix Model Technology II: Loops on the Lattice 9. Matrix Model Technology III: Free Fermions from the Lattice 10. Loops and States in Matrix Model Quantum Gravity 11. Loops and States in the $c=1$ Matrix Model 12. Fermi Sea Dynamics and Collective Field Theory 13. String scattering in two spacetime dimensions 14. Vertex Operator Calculations and Continuum Methods 15. Achievements, Disappointments, Future Prospects "if you read only one set of lecture notes this year, don't read these."