Detecting topology change via correlations and entanglement from gauge/gravity correspondence

Abstract

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.

arXiv comment48 pages. version in Journal of Mathematical Physics

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• BPS coherent states and localization
• Exciting LLM Geometries
• Coherent state operators, giant gravitons, and gauge-gravity correspondence
• Integrable Subsectors from Holography
• Coherent state excitations and string-added coherent states in gauge-gravity correspondence
• Scrambling in Yang-Mills
• Correlations vs connectivity in R-charge
• Semiclassical SL(2) Strings on LLM backgrounds
• Coherent state superpositions, entanglement and gauge/gravity correspondence
• Quantum Mechanics of Plancherel Growth
• Entanglement and mixed states of Young tableau states in gauge/gravity correspondence