Noncommutative solitons on Kahler manifolds

Details Noncommutative solitons on Kahler manifolds Noncommutative solitons on Kahler manifolds

2001-06-20

arxiv.org/abs/hep-th/0106180v3

JHEP 0203 (2002) 011

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, 3 figures, harvmac; references added

Scientific paper

10.1088/1126-6708/2002/03/011

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.

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