Projective modules over non-commutative tori: classification of modules with constant curvature connection

摘要

We study finitely generated projective modules over noncommutative tori. Weprove that for every module $E$ with constant curvature connection thecorresponding element $[E]$ of the K-group is a generalized quadratic exponentand, conversely, for every positive generalized quadratic exponent $\mu$ in theK-group one can find such a module $E$ with constant curvature connection that$[E] = \mu $. In physical words we give necessary and sufficient conditions forexistence of 1/2 BPS states in terms of topological numbers.