Noncommutative solitons on Kahler manifolds

Abstract

We construct a new class of scalar noncommutative multi-solitons on an arbitrary Kahler manifold by using Berezin's geometric approach to quantization and its generalization to deformation quantization. We analyze the stability condition which arises from the leading 1/hbar correction to the soliton energy and for homogeneous Kahler manifolds obtain that the stable solitons are given in terms of generalized coherent states. We apply this general formalism to a number of examples, which include the sphere, hyperbolic plane, torus and general symmetric bounded domains. As a general feature we notice that on homogeneous manifolds of positive curvature, solitons tend to attract each other, while if the curvature is negative they will repel each other. Applications of these results are discussed.

26 pages, 3 figures, harvmac; references added

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Cited by in corpus (9)

• Introduction to M(atrix) theory and noncommutative geometry, Part II
• D0-branes in Black Hole Attractors
• Introduction to Coherent States and Quantum Information Theory
• Study of charged gravastar model in $f(\mathcal{Q})$ gravity
• Loop amplitudes in maximal supergravity with manifest supersymmetry
• The Existence and Stability of Noncommutative Scalar Solitons
• On Coordinate Transformations in Planar Noncommutative Theories
• Scalar Solitons on the Fuzzy Sphere
• Noncommutative waves have infinite propagation speed