2015/01/31 by Andreas Karch, Christoph F. Uhlemann · 1 citation
Mathematics · Physics and Astronomy · #Anti-de Sitter space #Black Holes and Theoretical Physics #Conformal field theory #Conformal map #Conformal symmetry #Cosmology and Gravitation Theories #Coulomb #Entropy (arrow of time) #Gauge theory #Geometry #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum entanglement #Quantum mechanics #Space (punctuation) #Theoretical physics #hep-th
paper · pdf · doi:10.1103/physrevd.91.086005
published as Phys. Rev. D 91, 086005 (2015) · 11 pages, 6 figures; to appear in PRD
arxiv created 2015/03/23 · openalex publication_date 2015/04/06 · arxiv updated 2015/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We elaborate on the role of extremal surfaces probing the internal space in AdS/CFT dualities. Extremal surfaces in anti--de Sitter space quantify the ``geometric'' entanglement between different regions in physical space for the dual conformal field theory. This, however, is just one of many ways to split a given system into subsectors, and extremal surfaces in the internal space should similarly quantify entanglement between subsectors of the theory. For the case of AdS5\ifmmode×\else\texttimes\fiS5, their area was interpreted as entanglement entropy between U(n) and U(m) subsectors of U(n+m) N=4 super Yang-Mills theory (SYM). Making this proposal precise is subtle for a number of reasons, the most obvious being that from the bulk one usually has access to gauge-invariant quantities only, while a split into subgroups is inherently gauge variant. We study N=4 SYM on the Coulomb branch, where some of the issues can be mitigated and the proposal can be sharpened. Continuing back to the original AdS5\ifmmode×\else\texttimes\fiS5 geometry, we obtain a modified proposal, based on the relation of the internal space to the R-symmetry group.