Matrix models of string theory
String models Matrices
IOP Publishing
2018
EISBN 9780750317269
1. Introduction.
part I. String theory. 2. String theory.
2.1. Actions, symmetries and solutions.
2.2. Canonical quantization and Virasoro algebra.
2.3. Spurious states and critical strings.
2.4. Lightcone gauge quantization.
2.5. Exercises
3. Polyakov path integral.
3.1. Gauge fixing and Fadeev-Popov ghosts.
3.2. The energy-momentum tensor.
3.3. Quantization of the ghosts.
3.4. BRST symmetry.
3.5. Exercises
4. Introduction to conformal field theory.
4.1. The conformal groups SO(p + 1, q + 1).
4.2. The conformal group in two dimensions.
4.3. The energy-momentum tensor.
4.4. The operator product expansion.
4.5. Conformal field theory and BRST quantization.
4.6. Representation theory of the Virasoro algebra.
4.7. Theorem.
4.8. Exercises
5. Superstring theory essentials.
5.1. The superparticle.
5.2. The Green-Schwarz superstring.
5.3. The Ramond-Neveu-Schwarz superstring.
5.4. Canonical quantization.
5.5. The light cone/path integral quantization.
5.6. Other very important topics.
5.7. Exercises
part II. Matrix string theory. 6. A lightning introduction to superstring theory and some related topics.
6.1. Quantum black holes.
6.2. Some string theory and conformal field theory.
6.3. On Dp-branes and T-duality.
6.4. Quantum gravity in two dimensions.
6.5. Exercise
7. M-(atrix) theory and matrix string theory.
7.1. The quantized membrane.
7.2. The IKKT model or type IIB matrix model.
7.3. The BFSS model from dimensional reduction.
7.4. Introducing gauge/gravity duality.
7.5. Black hole unitarity from M-theory.
7.6. M-theory prediction for quantum black holes.
7.7. Matrix string theory.
7.8. The black hole and confinement phase transitions.
7.9. The discrete light-cone quantization (DLCQ) and infinite momentum frame (IMF).
7.10. M-(atrix) theory in pp-wave spacetimes.
7.11. Other matrix models.
7.12. Exercises
8. Type IIB matrix model.
8.1. The IKKT model in the Gaussian expansion method.
8.2. Yang-Mills matrix cosmology.
8.3. Emergent gravity : introductory remarks.
8.4. Fuzzy spheres and fuzzy CPn.
8.5. Fuzzy SN 4 : symplectic and Poisson structures.
8.6. Emergent matrix gravity.
8.7. Emergent quantum gravity from multitrace matrix models.
8.8. Exercise.
Appendix A. Algorithms and Monte Carlo codes for the matrix models of string theory.
Beginning with a systematic review of the standard exposition of string theory, which is required for a proper understanding of matrix models of string theory, this book proceeds to provide a comprehensive presentation of matrix models of string theory and their areas of applications. Supplemented with exercises and an appendix on Monte Carlo algorithms and methods used for matrix models of string theory this work provides both a valuable self-study guide for postgraduate students and a comprehensive review and reference guide for researchers.
part I. String theory. 2. String theory.
2.1. Actions, symmetries and solutions.
2.2. Canonical quantization and Virasoro algebra.
2.3. Spurious states and critical strings.
2.4. Lightcone gauge quantization.
2.5. Exercises
3. Polyakov path integral.
3.1. Gauge fixing and Fadeev-Popov ghosts.
3.2. The energy-momentum tensor.
3.3. Quantization of the ghosts.
3.4. BRST symmetry.
3.5. Exercises
4. Introduction to conformal field theory.
4.1. The conformal groups SO(p + 1, q + 1).
4.2. The conformal group in two dimensions.
4.3. The energy-momentum tensor.
4.4. The operator product expansion.
4.5. Conformal field theory and BRST quantization.
4.6. Representation theory of the Virasoro algebra.
4.7. Theorem.
4.8. Exercises
5. Superstring theory essentials.
5.1. The superparticle.
5.2. The Green-Schwarz superstring.
5.3. The Ramond-Neveu-Schwarz superstring.
5.4. Canonical quantization.
5.5. The light cone/path integral quantization.
5.6. Other very important topics.
5.7. Exercises
part II. Matrix string theory. 6. A lightning introduction to superstring theory and some related topics.
6.1. Quantum black holes.
6.2. Some string theory and conformal field theory.
6.3. On Dp-branes and T-duality.
6.4. Quantum gravity in two dimensions.
6.5. Exercise
7. M-(atrix) theory and matrix string theory.
7.1. The quantized membrane.
7.2. The IKKT model or type IIB matrix model.
7.3. The BFSS model from dimensional reduction.
7.4. Introducing gauge/gravity duality.
7.5. Black hole unitarity from M-theory.
7.6. M-theory prediction for quantum black holes.
7.7. Matrix string theory.
7.8. The black hole and confinement phase transitions.
7.9. The discrete light-cone quantization (DLCQ) and infinite momentum frame (IMF).
7.10. M-(atrix) theory in pp-wave spacetimes.
7.11. Other matrix models.
7.12. Exercises
8. Type IIB matrix model.
8.1. The IKKT model in the Gaussian expansion method.
8.2. Yang-Mills matrix cosmology.
8.3. Emergent gravity : introductory remarks.
8.4. Fuzzy spheres and fuzzy CPn.
8.5. Fuzzy SN 4 : symplectic and Poisson structures.
8.6. Emergent matrix gravity.
8.7. Emergent quantum gravity from multitrace matrix models.
8.8. Exercise.
Appendix A. Algorithms and Monte Carlo codes for the matrix models of string theory.
Beginning with a systematic review of the standard exposition of string theory, which is required for a proper understanding of matrix models of string theory, this book proceeds to provide a comprehensive presentation of matrix models of string theory and their areas of applications. Supplemented with exercises and an appendix on Monte Carlo algorithms and methods used for matrix models of string theory this work provides both a valuable self-study guide for postgraduate students and a comprehensive review and reference guide for researchers.
