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. Ex 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 BR 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 imp 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 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 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
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
Graduate students and researchers.
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Badis Ydri is currently a professor of theoretical particle physics, at the Institute of Physics, Annaba University, Algeria. He is also a research associate at the Dublin Institute for Advanced Studies, Dublin, Ireland, and a regular ICTP Assoc