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

Abstract

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

Latex. Misprints corrected

References in corpus (1)

• BPS states on noncommutative tori and duality

Cited by in corpus (7)

• Introduction to M(atrix) theory and noncommutative geometry
• Introduction to M(atrix) theory and noncommutative geometry, Part II
• Noncommutative Solitons on Orbifolds
• Moduli spaces of maximally supersymmetric solutions on noncommutative tori and noncommutative orbifolds
• Compactification of M(atrix) theory on noncommutative toroidal orbifolds
• 1/4-BPS states on noncommutative tori
• Gauge theories on noncommutative spaces