Quasicoherent states of noncommutative D2-branes, Aharonov-Bohm effect and quantum Mobius strip

Abstract: We find an analytical formula for the quasicoherent states of 3D fuzzy spaces defined by algebras generated by bosonic creation and annihilation operators. This one is expressed in a representation onto the coherent states of the CCR algebra. Such a fuzzy space can be assimilated to a noncommutative D2-brane of the M-theory (but also as a model of a qubit in contact with a bosonic environment). We apply this formula onto a D2-brane wrapped around an axis to obtain the geometry of a noncommutative cylinder. We show that the adiabatic transport of its quasicoherent states exhibits a topological effect similar to the Aharonov-Bohm effect. We study also a D2-brane wrapped and twisted to have the geometry of a noncommutative Mobius strip. Finally we briefly present the other two examples of a noncommutative torus and of a noncommutative Klein bottle.