@phdthesis{Northe2019,
  author    = {Northe, Christian},
  title     = {Interfaces and Information in Gauge/Gravity Duality},
  doi       = {10.25972/OPUS-19159},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-191594},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2019},
  abstract  = {This dissertation employs gauge/gravity duality to investigate features of ( 2 + 1 ) -dimensional quantum gravity in Anti-de Sitter space (AdS) and its relation to conformal field theory (CFT) in 1 + 1 dimensions. Concretely, we contribute to research on the frontier of gauge/gravity with condensed matter as well as the frontier with quantum informa- tion. The first research topic of this thesis is motivated by the Kondo model, which describes the screening of magnetic impurities in metals by conduction electrons at low temperatures. This process has a de- scription in the language of string theory via fluctuating surfaces in spacetime, called branes. At high temperatures the unscreened Kondo impurity is modelled by a stack of pointlike branes. At low tempera- tures this stack condenses into a single spherical, two-dimensional brane which embodies the screened impurity. This thesis demonstrates how this condensation process is naturally reinvoked in the holographic D1/D5 system. We find brane configu- rations mimicking the Kondo impurities at high and low energies and establish the corresponding brane condensation, where the brane grows two additional dimensions. We construct supergravity solutions, which fully take into account the effect of the brane on its surrounding space- time before and after the condensation takes place. This enables us to compute the full impurity entropies through which we confirm the validity of the g-theorem. The second research topic is rooted in the connection of geometry with quantum information. The motivation stems from the "complexity equals volume" proposal, which relates the volume of wormholes to the cicruit complexity of a thermal quantum state. We approach this proposal from a pragmatic point of view by studying the properties of certain volumes in gravity and their description in the CFT. We study subregion complexities, which are the volumes of the re- gions subtended by Ryu-Takayanagi (RT) geodesics. On the gravity side we reveal their topological properties in the vacuum and in ther- mal states, where they turn out to be temperature independent. On the field theory side we develop and proof a formula using kinematic space which computes subregion complexities without referencing the bulk. We apply our formula to global AdS 3 , the conical defect and a black hole. While entanglement, i.e. minimal boundary anchored geodesics, suffices to produce vacuum geometries, for the conical defect we also need geodesics windings non-trivially around the singularity. The black hole geometry requires additional thermal contributions.},
  subject      = {Information},
  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}
}