Non-linear sigma-models in noncommutative geometry: fields with values in finite spaces

Abstract

We study sigma-models on noncommutative spaces, notably on noncommutative tori. We construct instanton solutions carrying a nontrivial topological charge q and satisfying a Belavin-Polyakov bound. The moduli space of these instantons is conjectured to consists of an ordinary torus endowed with a complex structure times a projective space $C{P}^{q-1}$.

Latex, 10 pages

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Cited by in corpus (8)

• Holomorphic structures on the quantum projective line
• Sigma-model solitons on noncommutative spaces
• Star product formula of theta functions
• Lax pair and Darboux transformation of noncommutative U(N) principal chiral model
• Matrix Quantum Mechanics and Soliton Regularization of Noncommutative Field Theory
• Noncommutative Nonlinear Sigma Models and Integrability
• Functor of Points and Height Functions for Noncommutative Arakelov Geometry
• Twisted sigma-model solitons on the quantum projective line