We compute a momentum space version of the entanglement spectrum and entanglement entropy of general Young tableau states, and one-point functions on Young tableau states. These physical quantities are used to measure the topology of the dual spacetime geometries in the context of gauge/gravity correspondence. The idea that Young tableau states can be obtained by superposing coherent states is explicitly verified. In this quantum superposition, a topologically distinct geometry is produced by superposing states dual to geometries with a trivial topology. Furthermore we have a refined bound for the overlap between coherent states and the rectangular Young tableau state, by using the techniques of symmetric groups and representations. This bound is exponentially suppressed by the total edge length of the Young tableau. It is also found that the norm squared of the overlaps is bounded above by inverse powers of the exponential of the entanglement entropies. We also compute the overlaps between Young tableau states and other states including squeezed states and multi-mode entangled states which have similarities with those appeared in quantum information theory.
Geometric genus is an important invariant in the classification theory for isolated singularities. In
this paper we give a complete classification of three-dimensional isolated weighted homogeneous singularities with geometric genus one. This is one of important classes of minimally elliptic singularities.
F. BAUERMax Planck Institute for Mathematics in the SciencesF. CHUNGUniversity of California, San DiegoYong LinRenmin University of ChinaYuan LiuInstitute of Computational Mathematics and Scientific/Engineering Computing. Chinese Academy of Sciences
CombinatoricsGeometric Analysis and Geometric Topologymathscidoc:1804.06006
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 145, 2033-2042, 2017.1