@phdthesis{Gerbershagen2022,
  author    = {Gerbershagen, Marius},
  title     = {Quantum information and the emergence of spacetime in the AdS/CFT correspondence},
  doi       = {10.25972/OPUS-28199},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-281997},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2022},
  abstract  = {This thesis studies connections between quantum information measures and geometric features of spacetimes within the AdS/CFT correspondence. These studies are motivated by the idea that spacetime can be thought of as an effect emerging from an underlying entanglement structure in the AdS/CFT correspondence. In particular, I study generalized entanglement measures in two-dimensional conformal field theories and their holographic duals. Unlike the ordinary entanglement entropy of a spatial subregion typically used in the AdS/CFT context, the generalization considered here measures correlations between different fields as well as between spatial degrees of freedom. I present a new gauge invariant definition of the generalized entanglement entropy applicable to both mixed and pure states as well as explicit results for thermal states of the S_N-orbifold theory of the D1/D5 system. Along the way, I develop computation techniques for conformal blocks on the torus and apply them to the calculation of the ordinary entanglement entropy for large central charge CFTs at finite size and finite temperature. The generalized Ryu-Takayanagi formula arising from these studies provides further support for the idea that entanglement and geometry are intrinsically linked in AdS/CFT. The results show that the holographic dual to the generalized entanglement entropy given by the length of a geodesic winding around black hole horizons or naked singularities probes subregions of spacetime that are inaccessible to Ryu-Takayanagi surfaces, thereby solving the puzzle of how these features of the spacetime are encoded in the boundary theory. Furthermore, I investigate quantum circuits embedded in two-dimensional conformal field theories as well as computational complexity measures therein. These investigations are motivated by conjectures relating computational complexity in conformal field theories to geometric features of black hole geometries. In this thesis, I study quantum circuits built up from conformal transformations. I investigate examples of computational complexity measures in these circuits related to geometric actions on coadjoint orbits of the Virasoro group and to the Fubini-Study metric. I then work out relations between these computational complexity measures and the dual gravitational theory. Moreover, I construct a bulk dual to the circuits in consideration and use this construction to study geometric realizations of computational complexity measures from first principles. The results of this part on the one hand rule out some possibilities for dual realizations of computational complexity in two-dimensional CFTs put forward in previous work while on the other hand providing a new robust dual realization of a computational complexity measure based on the Fubini-Study distance.},
  subject      = {AdS-CFT-Korrespondenz},
  language  = {en}
}
@article{AbtErdmengerGerbershagenetal.2019,
  author    = {Abt, Raimond and Erdmenger, Johanna and Gerbershagen, Marius and Melby-Thompson, Charles M. and Northe, Christian},
  title     = {Holographic subregion complexity from kinematic space},
  series = {Journal of High Energy Physics},
  volume    = {1},
  journal   = {Journal of High Energy Physics},
  number    = {12},
  doi       = {10.1007/JHEP01(2019)012},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-227711},
  pages     = {1-35},
  year      = {2019},
  abstract  = {We consider the computation of volumes contained in a spatial slice of AdS(3) in terms of observables in a dual CFT. Our main tool is kinematic space, defined either from the bulk perspective as the space of oriented bulk geodesics, or from the CFT perspective as the space of entangling intervals. We give an explicit formula for the volume of a general region in a spatial slice of AdS(3) as an integral over kinematic space. For the region lying below a geodesic, we show how to write this volume purely in terms of entangling entropies in the dual CFT. This expression is perhaps most interesting in light of the complexity = volume proposal, which posits that complexity of holographic quantum states is computed by bulk volumes. An extension of this idea proposes that the holographic subregion complexity of an interval, defined as the volume under its Ryu-Takayanagi surface, is a measure of the complexity of the corresponding reduced density matrix. If this is true, our results give an explicit relationship between entanglement and subregion complexity in CFT, at least in the vacuum. We further extend many of our results to conical defect and BTZ black hole geometries.},
  language  = {en}
}