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Quantum entropy for the fuzzy sphere and its monopoles

A preprint version of the article is available at arXiv.

Abstract

Using generalized bosons, we construct the fuzzy sphere S 2 F and monopoles on S 2 F in a reducible representation of SU(2). The corresponding quantum states are naturally obtained using the GNS-construction. We show that there is an emergent nonabelian unitary gauge symmetry which is in the commutant of the algebra of observables. The quantum states are necessarily mixed and have non-vanishing von Neumann entropy, which increases monotonically under a bistochastic Markov map. The maximum value of the entropy has a simple relation to the degeneracy of the irreps that constitute the reducible representation that underlies the fuzzy sphere.

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Correspondence to Nirmalendu Acharyya.

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ArXiv ePrint: 1405.6471

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Acharyya, N., Chandra, N. & Vaidya, S. Quantum entropy for the fuzzy sphere and its monopoles. J. High Energ. Phys. 2014, 78 (2014). https://doi.org/10.1007/JHEP11(2014)078

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  • DOI: https://doi.org/10.1007/JHEP11(2014)078

Keywords

  • Solitons Monopoles and Instantons
  • Non-Commutative Geometry