Sigma-model solitons on noncommutative spaces

Abstract

We use results from time-frequency analysis and Gabor analysis to construct new classes of sigma-model solitons over the Moyal plane and over noncommutative tori, taken as source spaces, with a target space made of two points. A natural action functional leads to self-duality equations for projections in the source algebra. Solutions, having non-trivial topological content, are constructed via suitable Morita duality bimodules.

v2: minor changes

References in corpus (2)

• Inverse-Closedness of a Banach Algebra of Integral Operators on the Heisenberg Group
• Quantum theta functions and Gabor frames for modulation spaces

Cited by in corpus (7)

• Solitons of general topological charge over noncommutative tori
• The harmonic oscillator on the Moyal-Groenewold plane: an approach via Lie groups and twisted Weyl tuples
• A noncommutative catenoid
• A remark on the gauge action and noncommutative solitons
• Functor of Points and Height Functions for Noncommutative Arakelov Geometry
• Twisted sigma-model solitons on the quantum projective line
• Fourier transform, Schrödinger representation, and Heisenberg modules