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Holography and Quantum Information Theory: Complexity and T T Deformation

Zolfi, Hamed | 2020

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53622 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Karimipour, Vahid; Naseh, Ali
  7. Abstract:
  8. In this thesis we are going to show various relations between AdS/CFT correspondence and quantum information theory. For this aim we have a brief review about this correspondence and describe how one can derive linearized Einstein's equations using holographic prescription of entanglement entropy. It is explained how the quantum error correction concept can help us to solve the paradoxes due to extrapolate dictionary. After introducing $ T\overline{T} $ deformation and complexity, we use the path integral optimization approach of Takayanagi and collaborators to find the time slice of geometries dual to states in the $ T\overline{T} $-deformed two dimensional conformal field theories (CFTs). The obtained optimized geometries actually capture the entire bulk, which fits well with the integrability and expected UV completeness of $ T\overline{T} $-deformed CFTs. Motivated by $ T\overline{T} $ deformation of a conformal field theory we compute holographic complexity for a black brane solution with a cut off using ‘complexity=action’ proposal. In order to have a late time behavior consistent with Lloyd's bound one is forced to have a cut off behind the horizon whose value is fixed by the boundary cut off. Using this result, we compute holographic complexity for two dimensional AdS solutions where we get expected late times linear growth. It is in contrast with the naively computation which is done without assuming the cut off where the complexity approaches a constant at the late time. We extend this analysis to the charged black holes. Concretely, we find the value of this new cut off for charged small black hole solutions of Einstein-Hilbert-Maxwell theory, in which the proposed bound on the complexification is saturated. We also explore this new cut off in Gauss-Bonnet-Maxwell theory
  9. Keywords:
  10. Complexity ; Entanglement Entropy ; Gauge/Gravity Duality ; AdS/CFT Correspondence ; TT Deformation ; Quantum Error Correction

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