A mathematical introduction to string theory : variational problems, geometric and probabilistic methods

Part I. 1. Introduction 2. Topological and metric structures 3. Harmonic maps and global structures 4. Cauchy Riemann operators 5. Zeta function and heat kernel determinants 6. The Faddeev-Popov procedure 7. Determinant bundles 8. Chern classes of determinant bundles 9. Gaussian meaures and random fields 10. Functional quantization of the Hoegh-Krohn and Liouville model on a compact surface 11. Small time asymptotics for heat-kernel regularized determinants Part II. 1. Quantization by functional integrals 2. The Polyakov measure 3. Formal Lebesgue measures 4. Gaussian integration 5. The Faddeev-Popov procedure for bosonic strings 6. The Polyakov measure in non-critical dimension 7. The Polyakov measure in critical dimension d=26 8. Correlation functions.