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Topics in String Theory and Quantum Gravity

L. Alvarez-Gaume, M. A. Vazquez-Mozo

Abstract

These lectures present a general critical assessment of various frameworks for quantum gravity, with particular emphasis on string theory. The topics discussed cover field-theoretical approaches to quantum gravity, anomalies, bosonic and fermionic string theories, as well as some aspects of string phenomenology and black hole physics.

Topics in String Theory and Quantum Gravity

Abstract

These lectures present a general critical assessment of various frameworks for quantum gravity, with particular emphasis on string theory. The topics discussed cover field-theoretical approaches to quantum gravity, anomalies, bosonic and fermionic string theories, as well as some aspects of string phenomenology and black hole physics.

Paper Structure

This paper contains 43 sections, 626 equations, 23 figures, 1 table.

Table of Contents

  1. General Introduction
  2. Acknowledgements.
  3. A note on this revised version
  4. Field-theoretical approach to quantum gravity
  5. Linearized gravity
  6. Supergravity
  7. Kaluza-Klein theories
  8. Quantum field theory and classical gravity
  9. Euclidean approach to quantum gravity
  10. Canonical quantization of gravity
  11. Gravitational instantons
  12. Consistency conditions: anomalies
  13. Generalities about anomalies
  14. Spinors in $2n$ dimensions
  15. When can we expect to find anomalies?
  16. ...and 28 more sections

Figures (23)

  • Figure 1: The gravitational anomaly in two dimensions
  • Figure 2: The disc ${\cal D}$ which parametrizes the two-parameter family of gauge fields $A^{t,\theta}$ with polar coordinates $t,\theta$
  • Figure 3: Integration contours to compute the equal-radius commutator
  • Figure 4: Torus with modular parameter $\tau$
  • Figure 5: Fundamental vertex in string perturbation theory
  • ...and 18 more figures