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Aspects of Two and Three Dimensional Quantum Gravity

Mohammadi, Hossein | 2024

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 57705 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Faraji Astaneh, Amin
  7. Abstract:
  8. Gravity models in lower dimensions, particularly in two and three dimensions, are powerful tools for gaining a deeper understanding of the fundamental structure of gravitational and quantum theories. Three-dimensional gravity, due to its simpler and more controllable properties, provides a unique laboratory for studying the geometric and topological features of black holes, as well as the holographic nature of spacetime. On the other hand, two-dimensional gravity models, such as dilaton gravity, play a crucial role in exploring the dynamic mechanisms of horizons and phenomena like black hole evaporation. These models not only allow us to grasp the complexities of quantum gravity in a more accessible language but also pave the way for more advanced research within the framework of string theory and applications of the holographic principle. In this thesis, we conduct a comprehensive study of two-dimensional JT gravity, analyzing its properties at both the classical and quantum levels to gain a deeper insight into this foundational model. In the realm of three-dimensional gravity, we focus on its correspondence with gauge theories; in this context, we carefully define and elaborate on the asymptotic symmetry groups. For asymptotically anti-de Sitter and flat spacetimes, we examine these symmetries in detail to reveal their important connections with the geometric and physical structure. Finally, we delve into the partition function of three-dimensional asymptotically anti-de Sitter gravity, offering an in-depth analysis of the quantum aspects of this model and examining its results and applications comprehensively
  9. Keywords:
  10. Quantum Gravity ; Holography ; AdS/CFT Conjecture ; Quantum Field Theory ; Conformal Fields Theory ; Partition Function ; Three Dimensional Gravity ; Low Dimensional Quantum Gravity Model

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