Quantum Entropy for the Fuzzy Sphere and its Monopoles

Abstract

Using generalized bosons, we construct the fuzzy sphere $S_F^2$ and monopoles on $S_F^2$ 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 non-abelian 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.

21 pages, typos corrected

References in corpus (1)

• The fuzzy S^2 structure of M2-M5 systems in ABJM membrane theories

Cited by in corpus (2)

• Monopoles, Dirac operator and index theory for fuzzy $SU(3)/(U(1)\times U(1))$
• New Fuzzy Extra Dimensions from $SU(\mathcal{N})$ Gauge Theories