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Symplectic Symmetry, NHEG Algebra and Its Representation

Javadinezhad, Reza | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 48580 (04)
  4. University: Sharif University of Technology
  5. Department: physics
  6. Advisor(s): Bahmanabadi, Mahmoud; Sheikh Jabbari, Mohammad Mahdi
  7. Abstract:
  8. The phase space of the Near Horizon of Extremal Geometries has been studied in ”arXiv:1506.07181”. The phase space for the NHEGs consists of the space of all near horizon geometries with a given symmetry. Utilizing covariant phase space method we will build the symplectic two form on the phase space and will use it to define the notion of symplectic symmetry. The conserved charges corresponding to this symmetries form a symmetry algebra which is called NHEG algebra. It turns out that this algebra is a generalization of the celebrated Virasoro algebra. In this thesis we will first review necessary concepts for construction of the phase space of a Lagrangian field theory and will build the phase space for the asymptotic AdS3 gravitational systems. We will study both symplectic symmetry and Hamiltonian formalism for the AdS3 case. Afterwards we will study the representation of NHEG algebra on the torus and prove the uniqueness of central extension of this algebra. In the end the representations of the corresponding group to NHEG algebra will be studied by using coadjoint orbit method. The classification of the coadjoint orbits will play a leading role in defining the microstates of a blackhole
  9. Keywords:
  10. Near Horizon Extremal Geometry (NHEG) ; Symmetry ; Phase Space File ; Symplectic Symmety ; Coadjoint Orbits ; Central Extension

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